ONE HUNDRED LESSONS 
IN FRACTIONS 



A.Flanagan Company 

CHICAGO 









One Hundred Lessons 
in Fractions 


By 

H. S. ALSHOUSE 

Principal of Brownstown, Pennsylvania, Public Schools 


CHICAGO 

A. FLANAGAN COMPANY 


G)AI ^7 

.A H-(* 


USHARY of C0N6RESS1 
Two Gopie? Recetoc; * 

AUG 5 i30f j 

j/BDyrfcht Entry 1 

£,t<?<>7 t 

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COPY B. 

mr If till* Hi, IMH 


Copyright, 1907, 

BY 

A. Flanagan Company. 


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PREFACE 


This little book is designed either as a text for class use, 
or as a help for the burdened teacher who feels the need of 
additional problems and knows not where they may be 
found. My motto has been, “One step and then an¬ 
other.” I have aimed to give sufficient problems to 
insure the mastery of the one step before the other is at¬ 
tempted. The course has been tested with three different 
classes and the results have encouraged me to put the 
lessons in a form available to others. 

The first thirty-five lessons are suitable for beginners, 
the next forty are slightly more advanced while the last 
twenty-five lessons require considerable reasoning power 
as well as mastery of processes. 

In the hope that it may bring comfort to many a dis¬ 
tressed teacher, and prove serviceable and practical, the 
book is submitted. 


Cambria, Pa. 


H. S. Alshouse. 




One Hundred Lessons in Fractions 


LESSON 1 

A quart of milk is how many pints? 

A pint is what part of a quart? 

How many half-quarts in a quart? 

How many half-dollars in a dollar? 

How many half-dozens of eggs in a dozen of eggs? 
What is the relation of a quart to a pint? A quart is 
2 times a pint. 

What is the relation of a pint to a quart? A pint is \ 
of a quart. 

What is the relation of a nickel to a dime? 

What is the relation of a dollar to 50 cents? Of 50 
cents to a dollar? 

What is the relation of 2 inches to 4 inches? Of 3 
inches to 6 inches? 

What is the relation of 4 cents to 2 cents? Of 6 quarts 
to 3 quarts? 

What is the relation of 2 to 4? Of 3 to 6? Of 5 to 10? 
Of 10 to 20? 

What number is \ of 12? Of 16? 20? 18? 14? 

10? 8? 50? 100? 

How many half-dollars in 2 dollars? In 4 dollars? 6 
dollars? 8 dollars? 10 dollars? 

How many dollars in 6 half-dollars? 8 half-dollars? 
12 half-dollars? 18 half-dollars? 



6 


ONE HUNDRED LESSONS 


LESSON 2 


How many pints in a quart and a half-quart? 

How many pints in 2* quarts? In 3* quarts? 4* 
quarts? 5* quarts? 6* quarts? 7* quarts? 8* quarts? 
9* quarts? 

How many quarts in 3 pints? In 9 pints? 11 pints? 
7 pints? 19 pints? 13 pints? 15 pints? 17 pints? 

1. A can of beans is worth 12* cents. What are 2 
cans worth? 

2. A watch cost 9* dollars and a chain 2* dollars. 
What did both cost? 

3. A man earns $13* in a week. His son earns $4* in 
the same time. How much more does the father earn 
than the son? 

Copy and complete: 


17* qt. 
13* qt. 
12* qt. 
13* qt. 

104 qt. 
154 qt. 

10* qt. 
9* qt. 
7\ qt. 


? qt. 
? qt. 
? qt. 
? qt. 
? qt. 
? qt. 

? qt* 

? qt. 
? qt. 

10* qt. — 9* qt. = ? qt. 


- 9J qt. 

- 6* qt. 

- 3* qt. 

- 9* qt. 

- 6* qt. 

- 9* qt. 

- 2* qt. 
+ 6 qt. 
+ 8 qt. 


8i 

qt. 

+ 

7* 

qt. 

= ? qt. 

9J 

qt. 

+ 

4* 

qt. 

= ? qt. 

8* 

qt. 

+ 

5* 

qt. 

= ? qt. 

Vi 

qt. 

+ 

3* 

qt. 

= ? qt. 

Si 

qt. 

+ 

4* 

qt. 

= ? qt. 

2i 

qt. 

+ 

8 

qt. 

= ? qt. 

6i 

qt. 

+ 

10 

qt. 

= ? qt. 

144 

qt. 

- 

6 

qt. 

= ? qt. 

174 

qt. 

- 

10 

qt. 

= Tqt. 

10i 

qt. 

+ 

8 

qt. 

- ? qt. 


LESSON 3 

1. Lemons are selling at 20 cents a dozen. What is * 
of a dozen worth? 

2. I have $3* in silver half-dollars. How many pieces 
of money have I? 



IN FRACTIONS 


7 


3. A milkman sells \ gallon to each customer. How 
many can he supply if he has 6J gallons? 

4. Ralph had 13 dollars. He found \ as many as he 
had. How many did he find? How many dollars had he 
then? 


5. Mary bought 25 sticks of candy at J of a cent each. 
What did they all cost? 

Copy and complete: 

2 = t 

3 = i 

4 = ? 

54 — j 

2i = i 

6 = 2 

5 = i 

§4 = 2 

m = T 

34 = i 

8= , 

7 = i 

H = r 

84 = j 

44 = j 

10 = 2 

9 = i 


7i = 7 

6i = 7 

¥ = ? 

1 = ? 

1 = ? 

* = ? 

y = ? 

V = ? 

ft = 7 

y- = ? 

f = ? 

V- = ? 

V = ? 

1 = 7 

y- = ? 

V = ? 

* = ? 

1 = T 

V = ? 

¥ = ? 

LESSON 4 

¥ = ? 

«= ? 

Twenty-four sheets 

of paper 

make a quire. 

Robert 


has 9J sheets. How much less than a quire has he? 


A boy has 16 pages to write, 
many remain unwritten? 

Samuel had a twenty-dollar bill, 
coat. How much had he left? 
Copy and complete: 

6 qt. — li qt. = 

8 pt. — 2\ pt. = 

12 pt. — 8£ pt. = 

11 qt. — 9J qt. = ? qt. 

10 qt. - 5i qt. = ? qt. 

9 qt. - 8J qt. = ? qt. 


He writes 8£ pages. How 


He spent $6^ for 


? qt. 
? pt. 
? pt. 


10 

15 

12 

15 

11 

13 


% = 
6i = 
6i = 
7J = 
8J = 
6J = 


8 


ONE HUNDRED LESSONS 


16 pt. — 7J pt. = ? pt. 

13 pt. — 8J pt. = ? pt. 

14 qt. — qt. = ? qt. 

13 qt. — 5^ qt. = ? qt. 


15 — 9J = ? 
15 - 4J = ? 

13 - 7J = ? 

14 - 8J = ? 


LESSON 5 

John has 13 half-gallons of berries. How many gallons 
has he? 

I have 17 silver half-dollars. To how many dollars.are 
they equal? 

Sarah wrote ^ a page daily for 13 days. How many 
pages did she write? 

A boy worked 15 half-days. How many days’ work 
was that? 

A boy saves each month. How much does he save 
in a year? 

A caramel costs \ of a cent. How many can you buy 
with 9 cents? 


Copy and complete: 
Twenty halves = ? ones 
Thirteen halves = ? ones 
Sixteen halves = ? ones 
Twelve halves = ? ones 
Seventeen halves = ? ones 
Fifteen halves = ? ones 
Fourteen halves = ? ones 
Eighteen halves = ? ones 



V = ? 23 = ? 

= ? V = ? 


LESSON 6 

How many quarts in a gallon? 
A quart is what part of a gallon? 


IN FRACTIONS 


9 


A peck is what part of a bushel? 

Twenty-five cents is what part of a dollar? 

What is the relation of 2 to 8? Of 3 to 12? Of 4 to 16? 
Of 5 to 20? Of 6 to 24? Of 7 to 28? Of 8 to 32? Of 
9 to 36? Of 10 to 40? Of 25 to 100? 

How many fourths in anything? 

How many quarts in a half-gallon? 

How many quarter-dollars in $£? 

How many fourths in a half? 

Three quarts is what part of a gallon? 

One half of a half-gallon is what part of a gallon? £ of 

i = ? 

How many half-gallons in 3 quarts? 
f is how many times J? f -=- J = ? 

How many fourths in \ and J? 

How many quarts in If gallons? In If gallons? In 
If gallons? 

Draw a square and divide it into 4 equal parts. Show 
that f = f. 

Cut a half-apple into 2 pieces. What is each part called? 
Copy and Learn: 

1 = 4 f-ljxj i + i = f = i J + i-2 

i = i i °f i I - 1 = 1 f — i = i = 

LESSON 7 

1. How many quarts in If gallons? 2 gallons? 3 gal¬ 
lons? 2\ gallons? 2\ gallons? 2f gallons? 

2. How many quarts in 4 gallons? 3^ gallons? 3f 
gallons? 3f gallons? 

3. How many quarts in 5 gallons? 4J gallons? 6 gal¬ 
lons? gallons? 


10 


ONE HUNDRED LESSONS 


4. How many quarts in 7 gallons? 8 gallons? 9 gal 
Ions? 10 gallons? 


5. How many quarts 
gallons? 5J gallons? 
Copy and complete: 

in 

4j gallons? 61 gallons? 41 

11 = ( 

4 =* 

H 

= T 

4i = , 

42 = T 

2* -T 

6 “ T 

5 

= i 

8 =! 

= i 

3 = T 

21 = T 

3f 

= T 

51 = T 

52 = , 

2* = T 

If = T 

7 

= ¥ 

41 = i 

6J = T 

31 = T 

31 = t 

9 

= T 

61 = * 

62 - i 


LESSON 8 

How many quarts in 1 of a gallon and \ of a gallon? 

How many pecks in \ of a bushel and 1 of a 
bushel? 

How many quarter-dollars in a half-dollar and a quarter 
dollar? 

How many gallons in 5 quarts? J of 5 qt. = ? 

How many gallons in 7 quarts? J of 7 qt. = ? 

How many gallons in 9 quarts? J of 9 qt. = ? J of 
11 qt. = ? J of 13 qt. = ? J of 10 qt. = ? J of 6 qt. 
= ? 

How many quarts in J gal. + f gal.? 11 gal. + f gal.? 
If gal. + 1 gal.? 1J gal. - 1 gal.? 

Samuel had 17 quarter-dollars. How many dollars 
had he? 

Anna gave 1 of an apple to each of 10 girls. How many 
apples did she give away? 

What is 1 of 8? J of 12? J of 16? i of 28? 

What is 1 of 2? J of 3? J of 1? .J of 11? 


IN FRACTIONS 


11 


Copy and complete: 


Hhf 

CO 

II 

Y = ? 

Y = ? 

} = ? 

II 

•^3 

2 1 = ? 

4 

II 

•^3 

¥ = 

1 9 = ? 

4 

V 6 = ? 

4 

¥ = ? 

¥ = ? 

¥ = ? 

¥ = ? 

22 = ? 

4 

Y- 

¥«? 

26 = ? 

4 

i-r 

Y = ? 

2 6 ^ ? 

4 

23 = ? 

4 

¥ = ? 


14 = ? 

4 

Y = ? 

f = ? 

Y = ? 

¥ 3 = ? 

2 8 _ ? 

4 

v=? 



LESSON 9 

How many pints in a quart? 

How many quarts in a gallon? 

How many pints in a gallon? 

A pint is what part of a gallon? 

What is the relation of a pint to a gallon? Of 2 pints 
to a gallon? 

What is the relation of a pint to a quart? Of J of a 
gallon to \ of a gallon? 

What is the relation of a pint to 3 quarts? Of J of a 
gallon to | of a gallon? 

What is the relation of ^ of a gallon to £ of a gallon? 
Of \ of a gallon to J of a gallon? Of f of a gallon to £ of 
a gallon? 

What is the relation of 3 pints to a gallon? Of 5 pints? 
Of 7 pints? 

What is the relation of 2 to 16? Of 3 to 24? Of 32 
to 4? Of 40 to 5? 

A gallon of berries is worth 32 cents. What is a pint 
worth? What are 3 quarts worth? 

A pint of strawberries costs 6 cents. What is a gallon 
worth? What are 3 quarts worth? 

A quart of milk is worth 10 cents. What are two gal¬ 
lons worth? What are three pints worth? 


12 


ONE HUNDRED LESSONS 


LESSON 10 

A quart is what part of a gallon? 

A pint is what part of a quart? Of a gallon? 

What is \ of J? 1 of i? 

What is \ of l of an apple? \ of i of a bushel? J of 
i of a dollar? 

What part of a gallon is 2 pints? 4 pints? 6 pints? 
What part of a gallon is 3 pints? 5 pints? 7 pints? 
How many eighths of a gallon in \ of a gallon? \ of 
a gallon? J of a gallon? 

Draw an oblong 4 inches long and 2 inches wide. 
Divide it into 8 squares. 

Each square is what part of the oblong? 

How many eighths in { of the oblong? \ -r- £ = ? 
How many eighths in \ of the oblong? i J = ? 

How many eighths in J of the oblong? 1 % = ? 

LESSON 11 

Fold a square of paper into 8 equal triangles. 

Each triangle is what part of the square? 

What part of the square is 2 triangles? 3 triangles? 
4? 5? 6? 7? 8? 


Copy and complete: 

* + i - » i + t - ? 

t ~ 

» = T 

J - i - ? 

i + i = ? 

i + t - T 

1 - 

i - ? 

1 - * - r 

4 + f = -5 

i~ i = ? 

\ ~ 

i = T 

t - i = r 

i + f = 5 

l-i-r 

i ~ 

1= T 

1 - i = ? 

s + h = * 

i-i-t 

i - 

i = t 

«- i = » 

4 — f = ¥ 

2 x f = ? 

i - 

i = T 

i of 1 - ? 

h °f i = s 

i + i-r 

i + 

* = T 

i of } = ? 

5Xi= g 

4 X i = ? 

i of i = ? 

6 X i = ? 


IN FRACTIONS 


13 


LESSON 12 

1. Ten cents is 1 of Isaac’s money. What is \ of 
his money? 

2. One-eighth of a bushel is 4 quarts. How many 
quarts in } of a bushel? 

3. 1 of a bushel of corn cost 16 cents. What will 1 of 
a bushel cost? 

4. A pint of milk is worth 2 cents. What is } of a 
gallon worth? What is 1 of a gallon worth? 

5. J of a gallon of syrup cost 13 cents. What is f of 
a gallon worth? 

6. A bushel of potatoes cost 48 cents. What cost 1 
of 1 of a bushel? 

7. A piece of cloth cost 871 cents. It was sold for 
$1. How many cents were gained? 

8. A yard of ribbon costs $J. How many yards can 
be bought for $1}? 

9. f of a yard of cloth cost 36 cents. What is \ of a 
yard worth? j of a yard? A yard? 1{ yards? 11 
yards? 1} yards? 2 yards? 





LESSON 

13 




Copy and complete: 

2- 1 = ? 4 + 21 = ? 

6 


3i = ? 

7 + 

4f = ? 

3- 


2 

-H=? 

8 

- 

4i=? 

6 + 

31 = ? 

9- 

lf = ? 

7 

+ 8J = ? 

13 

- 

4| = ? 

7 - 

31 = ? 

13 — 

6|= ? 

14 

-54=? 

7 

- 

2J = ? 

8 - 

2f = ? 

11- 

31 = ? 

16 

-8i = ? 

9 

- 

4} = ? 

10 - 

61 = ? 

8 — 

6i = ? 

17 

— 81 = ? 

16 

- 

7| = ? 

13 - 

1| = ? 

18- 

9J = ? 

13 

+ 8f = ? 

2 

+ 

6i = ? 

71- 

2 =? 

131- 

6 =? 

12 

-3i = ? 

10 

- 

6f = ? 

131 — 

4 =? 


14 


ONE HUNDRED LESSONS 


20- 8f = ? 14 -6J=? 12 - 5J = ? 16 - 7£ = ? 
21 — 15j = ? 16|-8 =? 13i-10i = ? 10i + 10i = ? 

LESSON 14 

Count by halves to 20, thus: 1, 1^, 2, 2%, 3, etc. 
Count by fourths to 10, thus: J, 1, 1^, 1J, 1}, 2, etc. 

Count by eighths to 5, thus: J, J, f, f, j, J, 1, 1J, etc. 


Add, counting fractions as above: 


21 

41 

41 

91 

41 

91 

71 

61 

91 

81 

91 

41 

91 

91 

91 

31 

31 

21 

31 

11 

91 

81 

41 

41 

4i 

41 

21 

21 

91 

31 

31 

41 

41 

81 

91 

41 

9} 

41 

91 

41 

21 

31 

61 

51 

21 

91 

41 

91 

2i 

41 

31 

41 

71 

21 

81 

61 

51 

41 

51 

81 

31 

31 

21 

31 

41 

91 

21 

91 

81 

91 

11 

21 

91 

81 

Vi 

31 

41 

41 

41 

51 

21 

41 

41 

21 

3i 

31 

21 

31 

31 

31 

91 

51 

91 

11 

61 

91 

4i 

41 

91 

81 

91 

31 

8} 

91 

11 

21 

81 

11 

?! 

I! 

?! 

?! 

5 ! 

?! 

?! 

?! 

?! 

?! 

?! 

?! 

21 

81 

21 

21 

71 

31 

il 

81 

il 

21 

31 

41 


LESSON 15 

How many feet in a yard? 

Draw a line one yard long on the blackboard. Erase 
one foot. What part of the line was erased? 

Erase another foot. What part of the line remains? 
What part has been erased? 

A foot is what part of a yard? Two feet is what part 
of a yard? 

What is J of a yard? Of 2 yards? Of 3 yards? 



IN FRACTIONS 


15 


What is J of 6? Of 9? Of 12? 15? 18? 21? 24? 
27? 30? 

How many feet in 2 yards? In 3 yards? 4 yd.? 5 
yd.? 6 yd.? 7 yd.? 8 yd.? 9 yd.? 10 yd.? 

How many feet in 1J yards? If yards? 

How many yards in 4 feet? In 5 feet? 

How many feet in 4 of a yard? 

What part of a foot is \ of a yard? 

How many inches in a foot? 

How many inches in J of a yard? In § of a yard? In 
a yard? In 4 of a yard? In -J of a yard? In j of a yard? 
Complete: 

4 yd. — \ yd. = ? inches. f yd. — § yd. = ? inches. 

J yd. — 4 yd. = ? inches. 4 yd. — 4 yd. = ? inches. 

LESSON 16 

What is the relation of 1 foot to 1 yard? Of 1 yard to 

1 foot? 

How many feet in 4 of a yard? f of a yard? 

What is the relation of 2 feet to a yard? Of 1 yard to 

2 feet? 

What is the relation of 6 inches to 2 feet? Of 9 inches 
to a yard? 

What is the relation of 8 inches to 2 feet? Of a foot 
to 4 inches? 

What is the relation of 4 of a yard to 4 of a yard? Of 
4 of a yard to 4 of a yard? 

What is the relation of 2 to 6? Of 3 to 9? Of 4 to 12? 
Of 5 to 15? Of 6 to 18? Of 7 to 21? Of 10 to 30? Of 
8 to 24? Of 9 to 27? Of 25 to 75? Of $1.00 to $3. 
What is the relation of 6 to 8? Of 9 to 12? 


16 


ONE HUNDRED LESSONS 


What is the relation of 2 feet to 1J yards? Of 4J 
yards to 1J feet? 

What is the relation of J yard to 2 yards? Of 3J yards 
to 2 feet? 

If a foot of molding is worth \ of a cent, what are 1J 
yards worth? 

If a yard of silk cost 75 cents, what are 1J yards worth? 

At 2 cents a foot, what will 2§ yards of wire cost? 

How many yards of braid will bind a square rug 4 feet 


long? 





LESSON 17 


2J yd. = ? ft. 

2§ yd. = ? ft. 

29 ft. = ? yd. 

10 ft. = ? yd. 

9}yd. = ?ft. 

3J yd. = ? ft. 

7 ft. = ? yd. 

8 ft. = ? yd. 

5Jyd. = ?ft. 

6§ yd. = ? ft. 

20 ft. = ? yd. 

25 ft. = ? yd. 

7J yd. — ? ft. 

5J yd. = ? ft. 

16 ft. = ? yd. 

26 ft. = ? yd. 

3§ yd. = ? ft. 

8J yd. = ? ft. 

11 ft. = ? yd. 

22 ft. = ? yd. 

4J yd. = ? ft. 

6J yd. = ? ft. 

18 ft. = ? yd. 

13 ft. = ? yd. 

8§ yd. = ? ft. 

7§ yd. = ? ft. 

23 ft. = ? yd. 

17 ft. = ? yd. 

4§ yd. = ? ft. 

9J yd. = ? ft. 

14 ft. = ? yd. 

19 ft. = ? yd. 


LESSON 18 

In a pound of anything, except drugs, gold, silver and 
precious stones, there are 16 ounces. 

How many ounces in \ of a pound? In J of a pound? 
| of a pound? 

How many ounces in J of a pound? f of a pound? f 
lb.? \ lb.? 

How many ounces in 2 pounds? 3 lb.? 4 lb.? 5 lb.? 
6 lb.? 10 lb.? 

How many ounces in 1^ pounds? 2\ pounds? 3J 
lb.? 4} lb.? 


iHw oo !*- 1 


IN FRACTIONS 


17 


Four ounces of ginger is what part of a pound? 

Twelve ounces of maple sugar is what part of a pound? 

Copy and complete: 


^ lb. + i lb. = ? oz. 
\ lb. lb. = ? oz. 
J lb. — £ lb. = ? oz. 
lb. + f lb. = ? oz. 
lb. — + lb. = ? oz. 


£lb. + ilb. = ?oz. 
I lb. — | lb. = ? oz. 
| lb. + J lb. = ? oz. 
J lb. — J lb. = ? oz. 


i lb. — i lb. = ? oz. 
J lb. + J lb. = ? oz. 
| lb. — | lb. = ? oz. 


1 lb. + | lb. = ? oz. 


LESSON 19 

What is the relation of 4 ounces to a pound? Of a 
pound to 4 ounces? 

What is the relation of a 2-ounce weight to a pound 
weight? Of an 8-ounce weight to a pound weight? 

What is the relation of 12 ounces to a pound? Of a 
pound to 12 ounces? 

What is the relation of 10 ounces to a pound? Of 6 
oz.? Of 14 oz.? 

What is the relation of 10 ounces to 4 ounces? Of f 
of a pound to J of a pound? 

What is the relation of 14 ounces to 4 ounces? Of $ of 
a pound to \ of a pound? 

What is the relation of 4 ounces to 6 ounces? Of { of 
a pound to § of a pound? 

If a pound of sugar costs 8 cents, what will 8 ounces 
cost? 2 oz.? 6 oz.? 12 oz.? 14 oz.? 10 oz.? 4 oz.? 

If 4 ounces of tea cost 15 cents, what will 8 ounces 
cost? | lb.? i lb.? 

| is the relation of what to 8 ounces? 

§ is the relation of what to 12 ounces? 


18 


ONE HUNDRED LESSONS 


If you eat f lb. of butter a day, how long will If lb. last 
you? 

If you use 4 oz. of sugar a day, how long will J of a 
pound last? 

LESSON 20 

How many working days in a week? 

If a man works 1 day, what part of a week does he work? 
What is the relation of 6 inches to a yard? Of 2 inches 
to a foot? 

Divide an apple into 6 equal parts. 

What is each part called? 

How many sixths in £ of the apple? In f of the apple? 

Inf? 

Draw an oblong 3 inches long, 2 inches wide. 

Divide it into inch squares. 

Each square is what part of the oblong? 

How many sixths in f? J? f? 1? 

What is J of \ of an apple? £ of J = ? 
i of an apple is how much more than J of an apple? 

i ~ i=? 

f of an apple is how much more than £ of an apple? 

i-i = ? 

£ is what part of £ ? £ -s- £ = ? 

£ is what part of £? £ -4- £ = ? 

£ is what part off? £ of f = ? f -4- £ = ? 

How many sixths in 2 oranges? 2£ oranges? 2f or¬ 

anges? 2f oranges? 2£ oranges? 2| oranges? 

How many sixths in 3? 4? 5? 6? 7? 8? 9? 

How many sixths in J and J of f ? 

How many sixths in J and f of f ? 


IN FRACTIONS 


19 


Copy and complete: 

i + i = s i + 3 = e 4 X J = ^ 3 X i = s 

4 + i= 6 i + f= 6 4 + 4=6 I — f = s 

I 4 = $ 6x4=6 4 ~ 4 = 6 I — i = s 

§—•£ = * 3 x | = -§■ 4 — 4=6 4 — 4 = s 

Count by sixths to 5, thus 4? 4> 4? f, f, 1, 14> etc. 



LESSON 21 



Copy and complete: 




H - » i - » 

v = ? 

V = 7 

V 

= ? 14 = 5 

H - « V - ? 

V = 7 

V = 7 

V 

= 7 14 = 5 

34 = s V = ? 

V = 7 

4* = ? 

2 5 

if 

= 7 14 = 5 

4§ = v 4 = ? 

V = 7 

V s = 7 

V 

= ? 2 = * 

3J = T V - ? 

V = 7 

V = 7 

3 0 
¥ 

= ? 34 = * 

4 = * V = ? 

V = ?• 

V = 7 

V 

= ? 54 = 5 

94 + 74=? 94- 

■24=? 

84 + 74 = 

? 

174-84=? 

84 + 64 = ? 8§ — 

-54=? 

74 + 94 = 

:? 

164-74=? 

54+14 = ? 10J- 

-64=? 

44 + 84 = 

:? 

144-64 = ? 

24 + 24 = ? 114- 

-44=? 

64+74= 

:? 

154-84 = ? 

74 + 24 = ? 12|- 

-74=? 

94 + 84 = 

:? 

16# — 94 = ? 

94-14 = ? 9f - 

-44 = ? 

144-64 = 

’ ? 

144-64 = ? 

74-24 = ? 4|- 

-14=? 

134-14= 

= ? 

134-54=? 


LESSON 22 

Give the relation of a to b and b to a —thus, 3 is J of 12; 
12 is 4 times 3. 

a b a b a b 

3 12 9 12 12 24 

21 7 9 36 12 48 

12 16 6 24 6 9 


20 


OiV^ HUNDRED LESSONS 


a 


b 

a 

b 



a 

b 

8 


12 

16 

24 



9 

27 

5 


40 

25 

100 



4 

12 ' 

9 


18 

12 

24 



15 

30 

3 


24 

15 

20 


10 

15 

12 


18 

6 

36 



8 

32 

H 


3 

11 

4 



U 

5 

i 


1 

1 

1 



1 

i 

i 


1 

1 

1 



1 

i 

i 


1 

1 

I 



1 

i 




LESSON 23 





Copy and complete: 







i X 4 = 

? 

i of i 

= ? 

1 of 1 

= 

? 


i + i = 

i °f i = 

? 

i °f i 

= ? 

1 - 1 

= 

? 


2+ i = 

1 + * = 

? 

i + 1 

= ? 

’1 + 1 

= 

? 


1 + 1 - 

i ~ i — 

? 

t - i 

= ? 

1 °f S 

= 

? 


iof *- 

4 of | = 

? 

1 i 

= ? 

t + i 

= 

? 


l + i- 

3.1 _ 

4 “ 8 — 

?* 

1 + * 

= ? 

i - » 

= 

? 


t + i = 

1 of f = 

? 

i of | 

= ? 

f-i 

= 

? 


1 - i = 

i~l = 

? 

I ~ 1 

= ? 

1 — 1 

= 

? 


! - i - 

1 _ 4 _ 

2 8 — 

? 

1 _s_ 3 

2 • S 

= ? 

i - 1 

= 

? 


i + 1 = 

1 of 1 = 

? 

i of 2 

= ? 

1 of 3 

= 

? 


iof 5 = 

1X6 = 

? 

i X 4 

= ? 

1 X 4 

= 

? 


i X 5 = 

iof 5 = 

? 

iof 7 

= ? 

iof 3 

= 

? 


i of 1 = 

1 - 1 = 

? 

i + i 

= ? 

t + 1 

= 

? 


i + i = 

1 = ¥ 


i = 5 

1 = 

s 

i 

4 

= 

¥ 

i = 

1 = T 


i = s 

1 = 

$ 

1 

= 

¥ 

1 = 


*} -*• i is the same as | J. f is how many times 
i? f -s- J = ? In each division problem make the frac¬ 
tions similar by reducing to fourths, sixths, or eighths. 



IN FRACTIONS 


21 


LESSON 24 


How many inches in a foot? 

One inch is what part of a foot? 

Two inches is what part of a foot? 3 inches? 4 in.? 
5 in.? 6 in.? 7 in.? 8 in.? 9 in.? 10 in.? 11 in.? 
How many inches in J of a foot? 

How many twelfths of a foot in \ of a foot? ^V = ? 

How many inches in J of a foot? 

How many twelfths of a foot in J of a foot? i iV = ^ 
How many inches in £ of a foot? 

How many twelfths of a foot in J of a foot? J -f- T V = ? 
How many inches in J of a foot? 

How many twelfths of a foot in J of a foot? J -f- T V = ? 
How many inches in f of a foot? 

How many twelfths of a foot in | of a foot? f -f- = ? 

Draw an oblong 4 inches long, 3 inches wide. 

Divide it into inch squares. 

Each square is what part of the oblong? 

How many twelfths in \ of the oblong? In J of the 


oblong? §? i? 1? t? |? 
Count by twelfths to 5. 

Copy and complete: 


6 _ 

U — Y 

t ! = = n 



LESSON 25 


What is the relation of 2 inches to 4 inches? Of $ 
to 4? 

What is the relation of 5 inches to 10 inches? Of T 6 * 
to |? 


22 


ONE HUNDRED LESSONS 


What is the relation of 10 inches to 4 inches? Of f 
to J? 

How many months in J of a year? J yr.? \ yr.? J 
yr.? T V yr.? § yr.? | yr.? | yr.? 

What is the relation of 3 months to 1 month? Of \ 
to y 1 ^? 

What is the relation of 6 months to 9 months? Of \ 
to |? 

§ is the relation of what to 1 year? Of what to J year? 

4 is the relation of what to J yr.? Of what to 1 month? 

What is the relation of J to §? Of J to T V? Of \ to ^? 
Of l to 2? Of | to 1J? Of l to 1-i? Of i to 1J? Of i 
tolj? 

A boy lives in the city 4 months. What part of the 
year does he live in the country? 

Fred goes to school f of the year. How many months 
of vacation has he? 

When § of a line is erased, how many twelfths of the 
line remain? 

A man earns $400 in § of a year. What does he earn 
in a month? In § of a year? 

LESSON 26 


Copy and complete: 


if x 

2 

= 

? 

tV 

X 

5 - ? 

Ax 

7 

= 

? 

iV x 

9 = 

A x 

2 

= 

? 


of 

II 

•-<0 

4 of 

i 

— 

? 

iof 

f = 

i- 

tV 

= 

? 

4 


A = T 

1 + 

tV 

= 

? 

5 • 

■ 

tV = 

4- 

T2 

= 

? 

4 


A = ? 

3 _i. 

4 • 

3 

T? 

= 

? 

5 • 

¥ * 

tV = 

•i- 

* 

1 

6 

= 

? 

i 

-5- 

4 = i 

12 1" 

i 

= 

? 

tV ^ 

tV = 

tV x 

3 

= 

? 

tV 

X 

G = ? 

tV x 

8 

= 

? 

12 X 

10 - 

i of 

1 

6 

= 

? 

i 

4 

of 

1 _ ? 

S — • 

i of 

5 

6 

= 

? 

tV x 

11 = 




IN FRACTIONS 


23 


4 + 

iV = 

= ? 

4 

-A 

TJ 

= ? 

3 

4 

-4- 

A 

= ? 

4 of 

4 

= 

0 

4 

TJ = 

= ? 

§ 


4 

= ? 

5 

¥ 

-T- 

4 

= ? 

1 

-4- 

tV 

= 

? 

« + 

4 = 

= ? 

A 

-T- 

4 

= ? 

TJ 

-4- 

4 

= ? 

yj X 12 

= 

? 






LESSON 27 








Practice until you can 

answer readily 

: 






A + 

i _ 
4 — 

TJ 

1 

~ 

i i 
T2 

= ? 

1h 

- 

1 

T 

= ? 

44 

- 

4 

= 

? 

A + 

1 _ 

6 — 

T¥ 

T2 

+ 

4 

= ? 

TJ 

- 

1 

2 

= ’? 

1 

- 

4 

= 

? 

4 + i = 

T¥ 

4 + 

4 

= ? 

TJ 

- 

4 

= ? 

3 

4 

- 

4 

= 

? 

i + 

#- 

TJ 

4 + 

i 

= ? 

TJ 

- 

4 

= ? 

5 

¥ 

- 

4 

= 

? 

§ + 

2 _ 
4 — 

11 

4 

- 

A 

= ? 

T 2 

- 

4 

= ? 

5 

6 

- 

4 

= 

? 

i — 

4 = 

T¥ 

TJ 

+ 

4 

= ? 

f 

- 

tj 

= ? 

1 

- 

i 

= 

? 

tV + 

i = 

T¥ 

4 

+ 

i 

= ? 

1 

- 

4 

= ? 

1 

- 

4 

= 

? 

4 + 

4 = 

T¥ 

4 + 

f 

= ? 

4 

- 

2 

4 

= ? 

1 

- 

A 

= 

? 

i + 

5 _ 

6 — 

TJ 

4 

“ 

4 

= ? 

4 

- 

4 

= ? 

tV 

+ 

5 

¥ 

= 

? 

» + 

6 _ 

6 — 

TJ 

A 

+ 

1 

= ? 

l 

- 

1 

= ? 

4 

+ 

4 

= 

? 

4 + 

4 = 

TJ 

4 

+ 

4 

= ? 

l 

- 

4 

= ? 

4 

+ 

5 

¥ 

= 

? 

tj + 

4 = 

T¥ 

4 

+ 

4 

= ? 

l 

- 

4 

= ? 

4 

- 

iV 

= 

? 

4 + 2 = 

T2 

4 

- 

A 

= ? 

ij 

- 

4 

= ? 

4 

— 

4 

= 

? 

4 + 

4 — 

TJ 

1 

2 

- 

1 

4 

= ? 

TJ 

- 

i 

= ? 

TJ 

- 

4 

= 

? 

1 + 

f = 

TJ 

4 

- 

1 

2 

= ? 

tj 

- 

5 

¥ 

= ? 

TJ 

- 

4 

= 

? 

4 — 

4 = 

TJ 

§ 

- 

4 

= ? 

\i 

- 

4 

= ? 

TJ 

- 

1 

= 

? 

44- 

4 = 

TJ 

3 

4 

- 

tV 

= ? 

1 

- 

tV 

= ? 

f 

- 

A 

= 

? 

44 — 

4 = 

1 Z, 

5 

¥ 

~ 

tV 

= ? 

A + 

4 

= ? 

TJ 

- 

4 

= 

? 

4- 

4 = 

TJ 

1 

- 

4 

= ? 

1? 

+ 

4 

= ? 

TJ 

- 

4 

= 

? 

4 ~ 

4 = 

TJ 

1 

— 

1 

4 

= ? 

A + 

i 

= ? 

4 

— 

A 

= 

? 







LESSON 

28 









How many ones in \ 3 ? 

To make 1 one requires J. } makes 2 ones; - 1 / make 
4 ones, and V make 4 ones plus J or 4J. 



24 


ONE HUNDRED LESSONS 


How many ones in 


4? 

*? 

ttl 

18 ? 

5 * 

10 ? 

4 

1 5 ? 

T* • 

Y ? 


11 

Y 1 

V 1 

i? 

Y i 

ft? 

1? 

Y? 

i 1 

v? 

V 1 

10? 

10? 

¥ • 

V ? 

1? 

Y ? 

}1 

V 1 

V ? 

1 1 

13 ? 

4 

v? 

Y 1 

Y 1 

Y 1 

Y ? 


V ? 

18 ? 

4 

1? 

Y ? 

Hi 

¥ 1 

V 1 

V ? 

V ? 

n ? 

4 

II? 

Y T 

V ? 


LESSON 29 

Copy and complete: 


i + 4 - » 

i + 

6 

6' 

= 

? 

i + n = ? 

tY + § — 1 

4 + lY — 1 

« + 

i 

= 

? 

f + A = f 

l + * - ? 

4 + t-T 

? + 

i 

= 

? 

iY + tY = 1 

t + 44 = ? 

1 + iT 

§ + 

3 

4 

= 

? 

1+ t = ? 

tY + f = ? 

i + i = ? 

i + 

3 

4 

=- 

? 

14 + i = ? 

12 + A - ? 

! + 

4 + 

T2i 

= 

? 

1+ t-T 

H + 4 - t 

4 + 1 - ? 

§ + 

4 

= 

? 

tY + « - t 

tY+ *-? 

4 + 1 = ? 

§ + 

4 

= 

? 

1 + » = ? 

t'+ 4 - 1 




LESSON 30 



How many cents in a dime? 

A cent is what part of a dime? 

What is the relation of 3 cents to a dime? Of 7 cents? 
Of 9 cents? 

How*many cents in \ of a dime? 

How many tenths of a dime in \ of a dime? i ttf = ? 
What is the relation of 5 cents to 1 cent? Of ^ dime 
to T V of a dime? Of J to T V? Of ^ to 4? 

A dime is.how many times 2 cents? 

Two cents is what part of a dime? 

How many tenths of a dime in \ of a dime? 5 ^iV = ? 


IN FRACTIONS 


25 


What is the relation of 4 cents to a dime? Of 6 cents? 
Of 8 cents? 

What is the relation of \ to ? Of A to J ? Of f to 
tV? Of A to f ? Of f to yy? Of yV to f ? Of j to yV? 
Of yV to £? Of \ to f? 

If f of a dime buys 1 yard of ribbon, what length of 
ribbon will 2 cents pay for? 3 cents? 5 cents? 7 cents? 
9 cents? 

Draw an oblong 5 in. long, 2 in. wide. 

Divide it into inch squares. 

Each square is what part of the oblong? 

How many tenths in \ of the oblong? f? f? f? ^? 
Count by fifths to 10. 


Complete: 


io — ¥ to — ¥ 


LESSON 31 


Complete: 


i 

+ 

TO 

= 

? 

9 _ 
TO 

4 

¥ 

= 

? 

2 

¥ 

- 

A 

,= 

? 

2 4- 
¥ T- 

TO 

= 

? 

3 

10 

+ 

1 

= 

? 

¥ ~ 

TO 

= 

? 

2 

¥ 

+ 

TO 

= 

? 

i + 

3 

TO 

= 

? 

¥ 

- 

ro 

= 

? 

i + 

4 

5 

= 

? 

J 

+ 

TO 

= 

? 

2 _ 
¥ 

3 

TO 

= 

? 

A 

- 

1 

5 

= 

? 

* + 

TO 

= 

? 

3 

¥ 

+ 

A 

= 

? 

A ~ 

¥ 

= 

? 

A 

- 

i 

= 

? 

¥ + TO 

= 

? 

t 

+ 

i 

— 

? 


1 

TO 

= 

? 

A 

- 

t 

¥ 

= 

? 

I + 

TO 

= 

? 

A 

+ 

3 

¥ 

= 

? 

TO — 

i 

= 

? 


3 

5 

+ TO 

= 

? 

i 

- 

i 

= 

? 

4 

¥ 

1 

3- 

= 

? 

¥ 

+ 

i 

= 

? 

TO 

+ i 

= 

? 

A 

- 

3 

¥ 

= 

? 

i 

+ I 

= 

? 

3 

¥ 

- 

3 

T o 

= 

? 

i 

_ 2 

¥ 

= 

? 

¥ 

+ 

3 

TO 

= 

? 

1 

2 

+ A 

= 

? 

4 

- 

3 

TO 

= 

? 

9 

T o 

_ 2 
5 

= 

? 

A 

+ 

4 

¥ 

= 

? 

¥ 

+ TO 

= 

? 

3 

¥ 

- 



? 

A 

— i 

= 

? 

3 

TO 

+ 

4 

¥ 

= 

? 

3 

¥ 

+ A 

= 

? 

4 

¥ 

- 

1 

= 

? 

4 

¥ 

— TO 

= 

? 

i 

+ 

A 

— 

? 

i 

+ A 

= 

? 

A 

- 

3 

¥ 

= 

? 


26 


ONE HUNDRED LESSONS 






LESSON 

32 

4 of i-T 


TO 

-5- 

4=7 


i + lW 

i tV = ? 


iV 

-s- 

*-7 


1 TU = ? 

iof | = ? 


i 

of 

»-? 

9 2 _ ? 

TO • ¥ ' 

7 . 3 _ 

TO • ¥“ * 


lV 

-r- 

1 = 7 


t + A=? 

I of i=? 


i 

of 

1 = 7 


i of *-? 

7 1 _ ? 

T • J— ' 

- 

3 

¥ 

H- 

4=7 


4+ i=? 

i of tV~ ? 


¥ 

-T- 

A=? 


iof t-T 

2 • 3 _ ? 


4 


3 _ ?* 


3 JL — ? 

¥ “ 3 0 “ * 


■5 


TO — * 


5 * TO 

1 . 1 — ? 

2 ~ ¥ — * 


3 

¥ 

-T- 

4 = 7 


iof f = ? 

Ito = TTT 

14 

= 

T¥ 

4 = 

-5 

4 = 7 

= T¥ 

i A 

= 

TO 

2 = 

¥ 

H = ? 

lyo = ttj 

i A 


TO 

4 = 


U = ? 

If = TO 


= 

TO 

4 = 

¥ 

n = ? 

2 = TO 

1! 

= 

T¥ 

4 = 

■5 

4 = 7 


4 of 


i=? 


i Of I = ? 


A = ? 
4=7 
A=? 


t + 4=7 



LESSON 33 


Add: 


1. 

9tV> 

8tV> 

7tV? 

1© 







2. 

7 to 7 

9 t V, 

7toj 

2tV; 

3A, 

9to7 

9tV? 

8tV> 

7iV 


3. 

5ttt> 

2tV; 

4to> 

8 To 7 

9A- 






4. 


Si 7i 54. 








5. 

7i, : 

24, 4i, 64, 

■ 8J, 

94, 64, 44 

,2J, 

84, 94. 


6. 

9tV> 

8A. 

8^0 7 

Sto? 

9tV, 

8tV 

9to7 

9*, 

9 A, 

7tV- 

7. 

7-J, 5 j , 8J, 

44, 64, 74. 





8. 

7tV> 

2tV; 

9*, 

7tV> 

2tV? 

4*. 





9. 

9tV» 

9tV» 

6*, 

1 tV? 

2tV? 

ItV 

2tV; 

9t¥7 

2tV> 2fV? 

5A- 











10. 

6tV> 

7tV> 

4jV> 

7 tV> 

2tV> 

7iV> 

8tV, 

9tV- 



11. 

&tV> 

81V? 

^T¥» 

7*, 

2tV» 

6iV> 

2tV> 

^1^7 

1tV> 

2 t V 


e*|>© <m!>c 





IN FRACTIONS 


27 


12. 8}, 9§, 7\, 4, 5J, 6§, 7f, 4f. 

13. 8J, 9}, 3J, 4i 5J, 8J, 7*. 

14- 4i 5i 6f, 7i 81 9*, 7*. 

15. 8^, 9 t 5 ^, 4f\, 5yi, 6 t V, 8 t \, 9 jV 

16. 9^; 8ts, 7 T 1 0 , 8^, 1 {\, 8y<j. 

LESSON 34 

Draw a rectangle 5 inches by 4 inches. 

Divide it into inch squares. 

Each square is what part of the rectangle? 

How many twentieths in J of the rectangle? 

How many twentieths in j? ^? f? £? f? r V? A? A? 

» ? 

10 • 

Which is greater, £ or £? A or / 0 ? 

Erase \ and \ of the rectangles. How many twentieths 
remain? 

If John spends A of his money, what part of it remains? 
What is i of i? | of |? i of i? i of f? { of f? 
i of 1? iof T V? i Of A? i ofyV iof y\? 

Reduce to twentieths and add, subtract, and divide 
as indicated: 


i + i 

¥ — 

i 

3 _ 
¥ 

i 

i + 

i — to 

i+ i 

i “ 

VO 

f - 

" J 

i- 

is + TO 

i + tV 

i- 

TT) 

1 - 

2 

¥ 

i + 

4 _ 1 1 
¥ SS 

1 + 1 3 0 

4 _ 

5 

1 

ro " 

~ i 

TIT “ 

i+ I 

¥ + if 

2 

¥ 

So 

i- 

~ tV 

tV + 

So — l 

A + A 

TO “ 

i 


_ i 

i + 

if" 1 

i + A 

if — 

i 

1- 

" A 

4 _ 
¥ 

t V + i 

i + to 

11 _ 
SO 

i 

2 _ 
¥ 

" A 

TO + 

SO- + T 

i+ i 

n _ 
£0 

A 

TO ~ 

-H 

¥ — 

T¥ + if 

tV + if 

1 9 _ 
10 

1 

i- 

A 

i- 

3 i 3 
S+yu 



28 


ONE HUNDRED LESSONS 


LESSON 35 

1. Reduce \, and § to sixths. 

2. Reduce and j to eighths. 

3. Reduce b i) b b and £ to tenths. 

4. Reduce b h b b and £ to twelfths. 


5. Complete: 


i + J = ? i + i= ? 

i + t = » 


l + # = T 

f-l-T *-i-T 

t - i = T 


f- I - ? 

6. Complete: 

i + i + A = T 

i + i + 

i + 1- 1 

T + A + i = ? 

1 + I + tV 

+ 1 = ? 

* + i + A = ? 

A + i + 

l + i=? 

i + I + A = ? 

i + A + 

5 

6' 

+ f = ? 

7. Complete: 

1 + A - ' i = T 

i + tV — 

i 

- i = ? 

M*- 1 

+ 

®l 

1 

II 

ii ~ 1 + 

i 

- i- T 

A - 1 + i = ? 

i - i ~ A 

+ 1 = 7 

1 - i + * = ? 

i V + J + 

i 

- i= t 

8. Complete: 

8 X f = ? 3 X f = ? 

5 X f = ? 


3 X A = ? 

6 X i = ? 6 X f = ? 

8 X t o = ? 


2 X A = ? 

7 X 1 = ? 4 X i = ? 

4 X A = ? 


3XH=? 

3 X | = ? 5 X A■ = ? 

2 X A = ? 


9 X i = ? 

9. Complete: 

i of li = ? i of 2i = ? 

i of 2i = ? 


i of 8i = ? 

i of 2f = ? £ of I f = ? 

i of 4£ = ? 


i of 5J = ? 

* Of 2| = ? T V of 6§ = ? 

i of 9* = ? 


i of 6f = ? 


IN FRACTIONS 


29 


LESSON 36 

A number of equal parts of a unit is a fraction. 

The number written below the line is called the de¬ 
nominator. It shows into how many parts something 
has been divided. 

The number above the line is the numerator. It shows 
how many parts are taken. 

A fraction whose numerator is less than its denominator 
is a proper fraction. 

A fraction whose numerator is equal to or greater than 
its denominator is an improper fraction. 

A number consisting of a whole number and a fraction 
is called a mixed number. 

Tell whether the following are proper fractions, im¬ 
proper fractions, or mixed numbers: §, j, f, 1J, |, 4J, 
16 8 7 104137141 OJL 45 40 

How many thirds in an orange? 2 oranges? 2J 
oranges? 3 oranges? 3§ oranges? 

How many fourths in an apple? 2 apples? 2\ apples? 
3J apples? 4 apples? 

How many sixths in 5i? 4|? 8J? 3|? 7|? 

How many tenths in 2 t j q? 1 t 3 q? 4 t V? 5 t °o? 

How many twelfths in l t \? 2 A? 2A? 3H? 

Reduce 16J to thirds; 27j to fourths; 14J to eighths; 
14f to sixths; 8f to fifths; 9 x 7 o to tenths. 

How do we find that 4§ = -V 4 ? = V? 

Write a rule for reducing a mixed number to an im¬ 
proper fraction. 


30 


ONE HUNDRED LESSONS 


Reduce to improper fractions: 


25*- 

49 iV 

29! 

57f 

891 

94f 

27f 

68f 

42| 

78! 

76f 

67J 

16J 

24| 

CO 

s 

* 

45| 

89A 

72f 

23f 

361 

63 \ 

46J 

96f 

56! 


LESSON 37 

How many yards in of a yard? In y ? 

How many bushels in bushels? */? J y°? 

How many ones in - 1 /? -y*? - 1 /? \ 7 ? */-? -y ? 

20? 21? 24? 

TF- T0 r 

How do we find that J = 2J? that - 1 / = 3J? 

Write a rule for changing an improper fraction to a 
whole or mixed number. 

Reduce to whole or mixed numbers: 


1 5 3 

iji 

1 F 

w 

8 9 

3 

V 

V 


1 1 3 

~T~ 

12 8 

4 

H 

1.1 8 

3 

V 

1 1 8 

141. 

8 

V 

V 

2 3 0 

TIT 

V- 

H A 

4 1 

16 9. 

8 

10 8 

-y- 

■4* 

1 8 9 

TO 

1 1 6 

1 48 

16 6 


LESSON 38 

Reduce f, f, and to halves. 

Reduce !, yg, y!, y-|-, ! to thirds. 

Reduce f, y 9 ^, |f, and \\ to fourths. 

When a fraction is reduced to a fraction having the 
same value but with smaller terms, it is reduced to lower 
terms. 

To reduce to §, what must be done with both num¬ 
erator and denominator? 

To reduce f to j, what must be done? 

Write a rule for reducing a fraction to its lowest terms. 


IN FRACTIONS 31 


Reduce to lowest terms: 


it 

A 

if 

2 0 

HT 

it 


3 2 
¥0 

it 

1% 

1 4 

T8 

If 

3 0 

if 

2 0 
4 8 

1 8 

if 

1 6 
^4 

fo 

it 

H 

2 1 

2 0 

TO 

it 

li 


1 5 

8^ 

H 

if 




LESSON 39 





When fractions have the same number for a denominator 
they are said to have a common denominator. 

Reduce \ and f to eighths, § and f to twelfths. 

Reduce J and £ to twelfths. J and £ to tenths. 

In each problem what was done with both terms of 
the fractions? 

Reduce to fractions having the same denominator: 
f and | | and £ f and £ 

£ and | | and £ £ and £ 

f and f | and T V § and A 

For the common denominator we usually take the 
smallest number that can be exactly divided by each 
denominator. 

If we wish to reduce £ and f to fractions having the 
same denominator, 18 is the smallest number that can be 
divided by both 6 and 9; therefore we reduce to eighteenths. 

5X3 15 As 6 is contained in 18 3 times, to 

« ” 6X3 ~ 18 reduce £ to 18ths, we multiply both 
g 8X2 lg terms by 3; and as 9 is contained in 18 
"S’ — 9x2 — 18 2 times we multiply both terms of f 

by 2. 

Reduce to a common denominator : 

| and J § and | J and A 

fand i \ and £ t and H 




32 


ONE HUNDRED LESSONS 
> 


\ and 
4 and f 
I and T \ 
4 and | 
4 and | 


nr ana ¥ 
land | 
f and T 6 ^ 
4 and | 
l and 4 


4 and 
f and 
4 g and 
f and 


LESSON 40 

Reduce to improper fractions: 


5| 

91 

84 


154 

32J 

984 

6| 

74 

54 


24 f 

674 

57| 

3 A 

4f 

61 


184 

431 

46| 

Reduce to integers or mixed numbers: 



V 

4 8 

5 

V 

12 9 

V 


191 

3 2 

6 

2 6 

V 

168 

V 

tI 

9 8 

3 

W 

V 

V 

1 3 

2 

2 11 

~5~ 

A 4 4 

H 1 


Reduce to lowest terms : 


« 

W 

44 

iVo 

3 2 

8<J 

3 0 
¥8 

4 0 
15 

If 

5 4 

T2 

4f 

ft 

t 6 A 

3 2 

TO 

4 0 
4 8 

II 

H 

it 

11 

3 6 

14 

3 5 
6¥ 


Reduce to a common denominator: 

4, 1, 4 

5 11 

6, 4; T 

1, A, 4 


i. 4 

i 

i 

7 

T, 

4 

b 4 

f, 

4 

6, 

2 3 0, 

A 

4,1 

i, 

5 

6, 

1, 

H 

b 1 

4 

5, 

t, 

V5, 

rV 

1,4 

4, 

tV, 


44 

1, 4 

1, 

1, 

t4, 

A 


IN FRACTIONS 


33 


LESSON 41 

Only fractions having the same denominator can he added 
or subtracted. 

Reduce to a common denominator and add: 


f and i 

\ and | 

H and } 

i and f 

} and | 

f and f 

i and } 

i and T V 

tt and i 

\ and f 

i and T V 

t and l 

\ and n 

i and 

i and i 

\ and f 

i and } 

f and f 

J and f 

f and i 

4 and | 


LESSON 42 * 

Where the least common denominator is not readily 
found by inspection, we find the least common multiple 
of the denominators. 

Add i, j. 


2 

9 

3 

16 

6 

We divide by any prime factor 

3 

9 

3 

8 

3 

of two of the numbers writing be¬ 


3 

1 

8 

1 

low the quotients and the num- 


2 X 3 X 3X8=144 bers of which the divisor is not a 
factor. The product of the divis¬ 
ors and the remaining numbers is the least common 
denominator; hence the above fractions must be reduced 
to 144ths. 

Add: 


2 

5> 

5 

■g-J 

§ 

i 

h h 


i, 


i 



TIO 

Vo 


iVj 

4 

i 

To? tS> 


6 

"8) 

h 

il 

i, 


tV 

5 

tV; 

I 

h 

tV> 

i. 

1 





34 


ONE HUNDRED LESSONS 


ii> §> i §> 4> i> U 

$< \h is *> 4. f, i 

4, i * 1, A. f. 4 

ii> 4? 4 4}, 3}, 44> A 

4) rV> A A, 8§, J, 3* 

H» 4-A 61, 2J, t, 2* 

1> f> 4 7J, 94 , it, 4 

LESSON 43 

In adding mixed numbers the integers and the fractions 
should be added separately and the two sums added. 

Add 45J, 361, 27§. 

45 4 
36 1 

J7J 1 + 1 + 4 = 14+ & +41 = 41 = Hi 
108 
HI 

10941 

Add: 

1. 344,564,894,214. 

2. 85J, 73f, 564, 134- 

3. 728§, 3854, 6294, 8291- 

4. 2081, 57344, 3144, 228*. 

5. 1394, 3144, 1654, 328f. 

6. 532f, 1694, 2184, 758*. 

7. 6074, 218*, 803|, 7594. 

8. 357|, 528|, 7054, 809*. 

9. 875f, 672*, 342}, 124* 

10. 5734, 256f, 6924, 457*. 

11. 5454, 339§, 8264, 2674. 

12. 357J, 183}, 2344, 4564- 




IN FRACTIONS 


35 


13. 24*, 35*, 26§, 87f, 32*. 

14. 12*, 32*, 51*, 71*, 891. 

15. 6*, 3*. 9*, 4J, 3*, 8*. 

16. H, 4*, 8§, 5}, 5*, 8}. 

17. 7J, 8*. 1*, 7b 3*, 9*. 

18. 2f, 9*, 5*, 9*, 1J, 

4> iV 


LESSON 44 

Reduce to a common denominator and subtract: 


4 from f 


f from | 


f from } 

4 from T \ 


} from | 


4 from | 

4 f rom | 


t from 


f from | 

J from | 


4 from | 


f from 

i from 44 


§ from f 


i from | 

4 from f 


| from 4 


4 from 1 

4 from 4 


4 from j 


| from 44 



LESSON 45 



Subtract: 





1 ~ 4 

i 

-4 * - 

4 

T 9 0 — 4 

4 — 4 

4i 

— h i — 

10 

1 9 _ 3 
¥ 

1 — tV 

44 

2 5 _ 

T 6” 

2 

2 _ 1 
¥ T 

1-44 

4 

6 

-4 ii- 

4 

4 5 

11 — 

l - I 

5 

T 

-i tt - 

4 

t4 — 4 

i - § 

1 

— 4 44 - 

4 

4 — ts- 


LESSON 46 

Subtract 64J from 82. 

82 =.81 + 1 = 81f 
644 
17 * 


36 


ONE HUNDRED LESSONS 


Subtract: 


342 - 

124* 

853 - 

584} 

730 - 

386* 

573 - 

256} 

968 - 

686 } 

840 - 

549} 

692 - 

457}} 

839 - 

5961 

1,000 - 

* 

545 - 

339§ 

538 - 

395} 

1,000 - 

T oVc 

826 - 

267} 

600 - 

486f 

920 - 

919}} 

357 - 

183} 

830 - 

584* 

1,000 - 

** 

573 - 

259f 

540 - 

295| 

10,000 - 

909} 

748 - 

386f 

600 - 

393* 

6160 - 

100 * 



LESSON 47 




Subtract 24} from 54}. 

54} You cannot take } from f or j, so borrowing 1 
24} one (f) from the 4 ones, which with the | makes 
29} y, you then subtract-: * — } = }. 53 — 24 = 29. 


Subtract : 

342} - 124* 
573} - 256| 
692} - 457}} 
545} - 339§ 
826} - 267} 
357§ - 183} 
573} - 259f 


748* - 386f 
853* - 584} 
968§ - 686} 
839} - 596 f 
538f - 395} 
659} — 486 f-* 
839} - 584* 


547} - 295f 
658} - 383* 
735f - 386}} 
848} - 549} 
600} - 350* 
1,000} - 9} 


Find the value of: 

I + l- i + i 
t + I - i ~ i 
f + * — } — } 
!+}-}-} 

H - i + i + J 
\ — t + i + tV 
6 }+ 7 }+ 1 } — 9 } 
8f + 3}} + } - 10} 


LESSON 48 

2f + 9} + }-§§ 

7f - 2 } - 1} ^ 1} 

100 — 5} — 6} — 4* 

56 - 18* + 3} - 17* 
234} + 456} - 189} % 206} 
1,000 -‘208} - 94} - 186} 
1,000 - 208f + 94} - 186} 
1,000 - 79* + 56} - 780} 


IN FRACTIONS 


37 


LESSON 49 

1. A man bought a suit of clothes for $17} and a pair 
of shoes for $3}. How much had he left t if he had $25 
at first? 

2. From a web of cloth containing 60 yards 21J yards 
were sold. How many yards remained? 

3. One barrel contained 137} pounds of salt and an¬ 
other 99} pounds. How much more in the first barrel 
than in the second? 

4. A farmer sold 3 loads of hay for $14}, $16} and 
$18}, respectively. He received $40 cash. How much 
is still due him?' 

5. The sum of two numbers is 43|. One of the numbers 
is 17ft. What is the other number? 

6. Three men bought a horse. One man paid $14}, 
another $50}; the other as much as both. How much did 
the horse cost? 

7. Find perimeter or distance around a lot 86J ft. long 
and 45} ft. wide. 

8. Find perimeter of a room 28ft ft. long and 19f ft. 
wide. 

9. Find perimeter of a triangular field 41 }} ft. on a side. 

10. Find perimeter of a field whose sides are 85| ft., 
41} ft., 56} ft, and 87ft ft. 

11. Black had 180 acres of land. He sold 23f acres. 
How much remained? 

12. A man spent -ft of his money for a farm, ft for a 
house and ft for a horse. What part of his money was left? 

13. A man earns $100 a month. He pays for board 
$184, washing $2}, and for other expenses $19}. How 
much does he save per month? 


38 


ONE HUNDRED LESSONS 


14. From a farm of 100 acres two plots of 29^ acres 
each were sold. How much remained? 

15. How much greater is the perimeter of a field 48J 
rd. long and 16^ rd. wide, than that of a square field 32J 
rd. on a side? 

LESSON 50 

What is J of 8 cents? f of 8 cents? 

What is J of 9 dimes? § of 9 dimes? 

What is l of 10 dollars? f of 10 dollars? 


Complete: 


3 of 24 = ? 

3 of 24 = ? 

f of 20 = ? 

| of 100 = ? 

§ of 60 = ? 

| of 60 = ? 

f of 110 = ? 

f of 105 = ? 

§ of 72 = ? 

i of 88 = ? 

§ of 95 = ? 

| of 25 = ? 

3 of 90 = ? 

3 of 72 = ? 

f of 30 = ? 

| of 85 = ? 

$ of 50 = ? 

t of 155 = ? 

f of 40 = ? 

3 of 96 = ? 

i of 90 = ? 

i of 55 = ? 

f of 64 = ? 

3 of 48 = ? 

| of 32 = ? 

f of 88 = ? 

3 of 16 = ? 

| of 120 = ? 

f of 72 = ? 

f of 112 = ? 

i of 48 = ? 

3 of 200 = ? 


LESSON 51 


What is f 

of 13. f of 13 

= I X 13 = V 

= 5J 

Find the value of: 



3 of 25 

1 of 16 

| of 10 

A of 19 

f of 40 

f of 23 

f of 14 

A of 14 

§ of 31 

3 of 27 

1 of 20 

A of 23 

f of 14 

f of 13 

f of 12 

A of 34 

3 of 26 

i of 18 

| of 15 

A of 28 

| of 50 

| of 22 

3 of 26 

H of 25 

f of 19 

i of 31 

f of 19 

| of 30 

3 of 11 

3 of 17 

i of 11 

l of 34 


IN FRACTIONS 


39 


LESSON 52 


What is } of J? j of J? 

What is J of i? § of }? 

What is \ of i? J of %? 

What is i of |? | of J? | of J? 

What is | of f? }off? foff? ioiW ■ 
Multiply § by f, or find J of f. 

I* X = i , or § X i = A = i- 

2 


Find the value of: 


§ °f A 

1 of 

3 6 

3iT 

ix)| 

n x ei 

1 X 48 

i of 

A of 

4 

5 

}X1S 

n x ei 

HX 48 

§ °f A 

{of 

n 

3 v 8 

T A 33 

f X54 

£| X 64 

i of n 

! of if 


t x 2A 

H X 81 

tof H 

£ of 

1 8 

10 

M x n 

A x i\ 

A X 80 


LESSON 53 


Multiply: 
i X 151 
| X 137 
f X 126 
f X 781 
} X 193 


f X 480 
A X 171 
A X 282 
A x 486 
A X 560 


412 X f 
736 X § 
744 X 4 
400 X A 
616 X f 
189 X | 


728 X t 
823 X A 

1,000 x I 
1,000 x § 
1,000 x \ 

896 X A 


f X 211 

LESSON 54 

Multiply 369J by 24. 


369J 

24 J of 24 = 18. 

1476 We add the product of the fraction and multi- 
738 p p er to t he product of the whole numbers. 

8856 

18 


8874 




40 


ONE HUNDRED LESSONS 


Multiply: 




367J X 36 

727f X 35 


592f X 29 

820f X 24 ' 

668| X 24 


567f X 52 

441f x 28 

413f X 40 


812| X 39 

730J X 27 

623f X 32 


448| X 48 

417J X 36 

584f X 48 


769J X 66 

867| X 42 

493i X 49 


918| X 68 

537| X 25 

464f X 61 


558f X 57 


LESSON 55 



Multiply: 




875 X 64| 

285 X 17+f 


323 X 56f 

693 X 48 t 5 -j 

812 X 29f 


876 X 45| 

212 X 56 § 

625 X 36J 


989 X 39} 

985 X 73f 

625 X 34| 


676 X 45f 

896 X 27j 

254 X 28f 


798 X 28 t 6 5 

625 X 35JJ 

754 X 85§ 


1,000 X 34| 

939 X 34§ 

357 X 49f 


1,246 X 26§ 


LESSON 56 



Multiply, using cancellation where possible: 

i of f by 2 , 4 

1 7 

X 

i X 14 

i of | by 6 

« X 

2 2 v 1 0 

3 8 A 

14 by f of j 

1 2 
T 3 

X 

If X if 

14 by i of i 

2 3 

X if X If 

21 by § of ft 

1 6 
TT 

X 

16 X }| 

I of by 3J 

11 x 

n x n 

i of f by 20 

1 3 
T¥ 

X 

1 7 V 6 0 

IT A 

4 of | by +4 

1 2 

4 6 

X 

2 0 v 6 9 
a -jxr(r 

61 by J of ,V 6 s 

16. 

J4 

X 

11 x tVt 

4 of 12 by f 

9 

I 0 

X 

If x 


IN FRACTIONS 


41 


LESSON 57 

Find the cost of: 

1. 16 suites of furniture at $42} each. 

2. 8f lb. of meat at 16 cents per pound. 

3. 48§ acres of land at $56 per acre. 

4. 8 horses at $126J each. 

5. 37J yd. of carpet at 75<f a yard. 

6. 17 j gal. of oil at 13^ a gallon. 

7. 15f lb. meat at 14^ a pound. 

8. 38^ acres of land at $60 per acre. 

9. 14 cows at $36f each. 

10. 87J yd. of carpet at 80^ a yard. 

11. How many hours in 18J days? 

12. How many days in 48-f weeks? 

13. How many ounces in 28| lb.? 

14. How many minutes in 18 T 5 ^ hours? 

15. How many eggs in 36J dozen? 

16. How many cents in 56| dimes? 

17. How many days in 9| years? 

18. How many months in 71f years? 

19. A boy has f of an hour in which to study his lesson 
but plays § of the time. How long does he play? How 
long does he work? 

20. James has $6f, Henry has § as much plus $£. How 
much has Henry? 

21. A knife cost $T0 and a slate £ as much. What did 
both cost? 


LESSON 58 


Divide 4 by ^: 


2 8—90 
3J — 


28 = || = 4 


42 


ONE HUNDRED LESSONS 


Reduce to a common denominator and divide: 


1 + i ! + f 2 * + $ 

3 + 4 

* + 1 

i + 4 *+i *+# 

4 + | 

44-f 

l + i 4 + 1 A + » 

5 4- £ 

4 4-1} 

4^-f 7 4-} rf * 

-** i 

2i+ H 

l-l 4 + i } + l 

2i + A 

J + 3* 

LESSON 59 



What is | of 20? 20 4 - 5 = ? 



What is £ of 48? 48 - 5 - 6 = ? 



What is T V of 84? 84 4- 12 = ? 



What is £ of 3£? 3£ 4 - 4 = ? 



What is £ of 7£? 7£ 4 - 6 = ? 



.Find 2/ie value oj: 



4 v 3 5£ 4- 7 

3* - 

- 4 

6£ 4- 5 4* 4- 13 

84- 

- 5 

8} 4- 4 6| 4- 4 

5* - 

- 7 

7} - 9 2£ 4- 8 

84 - 

- 11 

4*-2 8*4- 5 

9f - 

-11 

5* 4- 4 7yV 4- 6 

4rV- 

- 11 

6* 4- 9 5* 4-19 

84- 

- 9 

LESSON 60 



How often is f contained in 10? 

What is § of 10? 

How often is - 1 / contained in 20? 

A of 20 = ? 

How often is £ contained in 14? 

4 of 14 = ? 

How often is 1£ contained in 12? 

f of 12 = ? 

How often is 1£ contained in 12? 

1 of 12 = ? 


Dividing a number by } is the same as multiplying it by 
what fraction? 

Dividing a number by If is the same as multiplying it 
by what fraction? 










IN FRACTIONS 


43 


27 -h If = 27 X 7 
30 -4- 3} = 30 X ? 
f of 36 = 36 -4- ? 

A of 52 = 52 -4- ? 

Divide: 

984 h- 1J 720 + 1§ 

345 -=- li 945 -h 1| 

429 -4- 34 855 -h 3f 

944 -4- If 855 h- If 

973 h- 1* 957 -4- If 

882 -4- 34 711 h- 44 


15 -4- 1§ = 15 X 7 
24 h- 2| = 24 X ? 
T \ of 44 = 44 h- ? 
t 4 j of 60 = 60 -4- 7 


875 -4-21 H + 3f 

612 h- 21 41 -4- 2f 

558 -4- If If 4- If 
825 h- 2f |f h- 2f 
832 + 24 If -4-' 24 
616 -4- 54 tV« -4- 74 


LESSON 61 

Find the value of: 

} | -4- 2 i of t 4 j -4- 35 

14 -4- 22 4 of 4J -4- 6 

5f -4- 4 64 -4- i of 20 

5§ 4- 7 284 t \ -4- 15 

3| -4- 8 349| h- 15 

| of f -4- 18 58,5901 h- 7 

| of 12 h- 80 56,7711 -4- 8 


35,492f -4- 6 
85,7511-4- 5 
25,7611 h- 3 
743,4161 -4- 6 
32,5581 -4- 3 
42,3561 -4- 7 


LESSON 62 

Find the value of: 

18-4-f 4,897 -4-f 34 h- 41 76,560 -4- If 

30 -4- 4 7,579 -4- 1 91 -4- 21 96,814 -4- I f 

144 -4- if 9,837 -4-f 95 -4- 3f 54,381 -4- If 

128 -4- f 46,811 -4- f 2,346 -4- 2f 65,492 -4- If 

361 -4-ff 75,460 -4- f 46,851 -4- 4f 80,000 h- 7f 



44 - 


ONE HUNDRED LESSONS 


Find the value of: 

i 


6 9 
f 0 IF 


41 


TO 


115 

2?6 


TO S ~T Al 
If - * 5 t 

19 J76 


?4? 


I °f f + * 

f of 12 -h * 


LESSON 

63 

l of - 

4 

nr ■ 

2 

4 of 4f - 


H -*■ 

|of il 

6 * + 

iof 9 

t 9 o X 

2 0 
?T 

_i_ 1 2 

' 13 

if x 

1 1 

T2 

+ ii 

1 2 • 
4T ~ 

11 

4 0 

X if 

1 3 • 

T 2 ~ 

1 5 
IT 

V 6 8 


n + 3i 
2f + 5* 
24f - 12* 
25* + 36* 
33* - 2* 
17* - 13* 
15* - 46* 
7 A -5“ 32* 


LESSON 64 

1. A man spends f of the day in work. In what time 
will he spend 15 days in work? 

2. If a train moves § of a mile each minute, in what 
time will it go 30 miles? 

3. How many books at $lf each can be bought for 

$ 12 |? 

4. If a man earns $2* a day, in what time will he earn 
$13*? 

5. How many yards of ribbon at 5* cents a yard can be 
bought for $47*? 

6. Into how many pieces 3* ft. long can a board 16* 
ft. long be divided? 

7. A teacher receives $367* for teaching 7 months. 
What are his wages per month? 

8. If 4 tons of coal cost $8f, how many tons can be 
bought for$17f? 

9. How many acres of land at $26* an acre can be 
bought for$106? 




IN FRACTIONS 


45 


10. A barrel contains 2f bu. of apple. How many 
such barrels will 61 f bushels fill? 

11. A man earns $2£ per day. In what time can he 
earn $9£ ? 

12. The product of two numbers is If. One number 
is If. What is the other number? 

13. If shoes that cost $3f are sold at f of cost, how many 
pairs can be bought for $117? 

14. If a dozen oranges cost 30 cents, how many oranges 
can be bought for $1? 

LESSON 65 

1. Richard had $£ and his brother had $1 T V How 
much had both? 

2. A yard of cloth cost $f. How many yards can be 
bought for $4f ? 

3. I bought f lb. of sulphur at 2 cents an ounce. What 
did the sulphur cost? 

4. I have $2£ and my friend has $}£• My money is 
how many times his? His money is what part of mine? 

5. James is 36 miles from home. Returning he walks 
i of the distance and rides the remainder of the distance. 
How far did he ride? 

6. A geography costs $1.20, a reader \ as much, and a 
notebook £ as much. What did all cost? 

7. A fruit dealer sells J of his oranges and has 12 dozen 
left. How much had he at first? 

8. Arthur bought 36 pens and sold T 5 * of them. How 
many remained? 

9. If 2£ yards of cloth cost 25 cents, what will 9£ yards 
cost? 


46 


ONE HUNDRED LESSONS 


10. How many sacks holding } lb. each will 241 lb. of 
candy fill? 

11. If a man travels 31 mi. in 7j hours, how far will 
he travel in 9} hours? 

12. If 9f tons of hay cost $115}, how many tons can be 
bought for $60? 

13. How many pounds of butter at $ v ^ a pound will 
pay for 16 dozen eggs at 22} cents a dozen? 

LESSON 66 

Reduce to improper fractions: 


137J 189f 

218| 318| 

2171 145 f V 

173| 268A 

Reduce to integers or mixed numbers: 

46 8 184 1_ 

^ 6 

189 1134 

J 

1381 2144 

T~ ¥ — 

48 15. 316 4 

6 6 

Reduce to lowest terms: 


4 4 16 8 

t?o -g-gir 

11 8 0 

Til 

120 108 

S8¥ ryy 

ffVs m 

Find the value of: 


§+!+£+} 
i + i + A + A 
f + £ + tV + A 
A + $ + T V + } 

18f + 9J 4- 164 
12f + 18J + 71 

7| + 19 A + 12f 
11A + 34| + 18ii 

Find the value of: 


A-i n-i 

t i } — f 

16 — 7| 9 A — 44 

13 - 8| 84 - 3| 


IN FRACTIONS 


47 


Find the value of: 


4 x | X X || 
t X 4 X §4 X J4 

4 x H x |i x A 

5 v 1 2 v 1 1 V 1 
¥ A TT A TO A S3 

Find the value of: 

t + i 4+1 

4 + i 41-3-3 


284A X 15 
349f X 21 
256| X 12 
196 A X 20 


31 + 4 71 - 5-31 

8-4 2j — 54 


Add: 


LESSON 67 


36f + 32f + 704 853| 

91§ + 57| + 464 638| 

754 + 38f + 37| 7184 

46 § + 56 j + 80 A 837f 

Subtract: 

921 l - 3454 837 

718f - 3274 627 

8024 - 7174 365 

5604 - 315| 3724 


+ 259f 
+ 794f 
+ 469* 
+ 752| 


- 365f 

- 4584 

- 180f 

- 1754 


Multiply: 

36J X 18 
41J X 24 
78 X 49f 
96 X 37f 


A x 24 x A 
11 x 6 X. 44 

24 X f X2§ 

I x A X 4f 


Divide: 

61 + 21 
41 + 21 
44 + If 
8-14 


624f - 4 
3654 - 5 
720 A + 8 
546J -r- 7 



48 


ONE HUNDRED LESSONS 


LESSON 68 

Give relation of a to b and b to a. 


a 

b 

a 

b 

a 

b 

3 

9 

9 

45 

12 

36 

21 

24 

9 

15 

12 

30 

12 

18 

6 

15 

6 

14 

8 

20 

16 

28 

9 

21 

5 

30 

25 

40 

4 

10 

9 

33 

12 

20 

15 

25 

3 

21 

15 

40 

10 

25 

11 

33 

13 

26 

26 

46 

18 

32 

14 

35 

21 

35 




LESSON 

69 



Give ratio of a to b and b to a. 




a 

b 

a 

b 

a 

6 

i 

i 

t 

s 

i 

3 

TH 

1 

i 

i 

3 

i 

A 


i 

2 0 

2 

5 

i 

\ 

i 

i 

lV 

i 

2o 

i 

2 

5 

3 

4 

* 

i 

2 

5 

1 

T 

i 

5 

S 

i 

lV 

4 

■& 

i 

1 

i 

2 

tV 

4 

3 

i 

§ 

I 

4 

5 

i 

i 

§ 

i 

H 

4 

A 

A 

3 

¥ 

3 

J 

A 

10 

1 

6§ 

if 

i 

1 

2 

5 

6 

4 

4 

¥ 

6 

¥ 

■ i 

1 0 

T 2 

2f 

H 

$6§ 

$4 


IN FRACTIONS 


49 


LESSON 70 

What is the ratio of: 

8 to 14? 15 to 21? 14 to 20? 

16 to 20? 18 to 24? 15 to 25? 

18 to 30? 16 to 18? 18 to 27? 

10 to 18? 16 to 28? 15 to 18? 


20 to 25? 
20 to 24? 
10 to 12? 
12 to 21? 


What will 16 books cost, if 20 books cost $18? The 
ratio of 16 to 20 is f. The cost is f of $18, or $14f. 

What will 10 knives cost, if 18 knives cost $24? 

If 14 pencils are worth 35 cents, what are 8 pencils 
worth? 

If 20 peaches are worth 24 oranges, how many oranges 
are 14 peaches worth? 

If 27 pigs cost $30, what will 18 pigs cost? 

If 28 tons of hay cost $301, what will 16 tons cost? 

If 21 sheep cost $54, what will 15 sheep cost? 

If 24 lamps cost $10.80, what will 20 lamps cost? 

If 18 oranges cost 45 cents, what will 15 oranges cost? 

If 24 bottles of ink cost 64 cents, what will 18 bottles 
of ink cost? 


LESSON 71 

1. If 10 suits of clothes cost $185, what will 8 suits 
cost at the same rate? 

2. If 30 panes of glass cost $13.80, what will 25 panes 
cost? 

3. If 8 sideboards cost $102, what will 6 sideboards cost? 

4. If 15 bushels of com cost $12.75, what will 12 bushels 
cost? 

5. If 24 bushels of wheat cost $17.28, what will 18 
bushels cost? 


50 


ONE HUNDRED LESSONS 


6. If 6 kitchen stoves cost $214.50, what will 4 stoves 
cost? 

7. If 18 cupboards cost $166.50, what will 14 cupboards 
cost? 

8. If 24 ladies’ silk coats cost $576, what will 15 coats cost? 

9. If a dozen Nottingham lace curtains cost $23.76, 
what will 8 curtains cost? 

10. If 16 bed spreads cost $23.68, what will a dozen 
bed spreads cost? 

11. If 27 yards of black crepe cost $36.45, what will 
15 yards cost? 

12. If 30 baby carriages cost $405, what will 8 carriages 
cost? 

13. If 18 Elgin watches cost $270, what will 15 watches 
cost? 

14. If 3 dozen mocha gloves cost $43.20, what will a 
dozen gloves cost? 

15. If 33 dinner sets cost $239.25, what will 18 dinner 
sets cost? 

^ 16. If 45 pigs cost $101.25, what will 18 pigs cost? 

LESSON 72 

6 is f of what number? 

If f of some number is 6, f of that number is 3, and §, 
or that number, is 9. 

Find the number of which 


12isJ 

15 isf 

12 is f 

16 is f 

8 is § 

10 isf 

24 isf 

12 isf 

12 isf 

16 isf 

30 isf 

48 is f 

10 is 4 

14 isf 

20 is f 

35 is J 

12 is 4 

12 isf 

15 isf 

18 is f 

8 is| 

10 isf 

20 isf 

40 is f 


nr FRACTIONS 


51 


LESSON 73 

1. A horse was sold for $210. This was J of what it 
eost. What did the horse cost? 

2. f of a ton of coal is sold for $1.80. What will a 
ton cost? 

3. $40 is ^ of the cost of a horse. What did the horse 
cost? 

4. A owns § of a farm. If his share is worth $2400, 
what is the farm worth? 

5. f of A’s wheat crop is 48 bu. 3 pk. How many 
bushels has he? 

6. A train runs 36 miles in f of an hour. How far will 
it run in 2f hours? 

7; t 8 t of a square rod contains 22 sq. yd. How many 
square yards in a square rod? 

8. I spent r 5 2 of my money and had $420 left. How 
much had I at first? 

9. If | of a ton of hay cost $7.20, what will 8 tons cost? 

10. A family uses f of a sack of flour in 2 weeks. How 
long will 8 sacks last? 

11. A merchant was obliged to sell some flour at f of 
its cost. If he sold it at $4.80 a barrel, what did it cost 
him? 

12. A furniture dealer lost X V of its cost in selling a 
couch for $14.85. What did it cost? If he had gained 
T v, for what would he have sold it? 

13. $120 is | of what a farmer received for a horse and 
cow. If he received 4 times as much for the horse as for 
the cow, what did he get for each? 

14. I have $24J. This is } of what my brother has. 
How much has ray brother? 


52 


ONE HUNDRED LESSONS 


LESSON 74 

Find the number of which 


75 is f 

125 is f 

330 is 44 

468 is 

80 is | 

340 is if 

280 is 1 

375 is 

72 is f 

560 is | 

315 is 4 

816 is 

84 is f 

300 is 

' 372 is J 

656 is 

96 is f 

240 is 4| 

296 is § 

720 is 


LESSON 75 

1. A second-hand bicycle was sold for $20. If that 
was f of its cost, what did it cost? 

2. A man paid $3.45 a month for his lodging, which 
was T \ of the cost of his meals. What was the cost of 
both? 

3. If f of a yard of silk cost 60 cents, what will 5j 
yards cost? 

4. If f of a mill is worth $4,885, what is the value of 
the whole mill? 

5. If J of a yard of cloth cost 48 cents, what will 5 pieces 
each containing 12 yards cost? 

6. A way train runs 175 miles in 5 hours. This is only 
| of the distance a fast express train can run in the same 
time. How far does the fast train run in an hour? 

7. $140 is 4 of the cost of a horse, and a carriage cost 4 
as much. What did both cost? 

8. After buying some provisions I had $354 left. This 
is f of what I had at first. How much had I? 

9. A gardener set out some plants of which 120 lived. 
That was of the number set out. How many did he 
set out? 


IN FRACTIONS 


53 


10. $3$ is A of my money. How much money have I? 

11. After spending \ of my money, I had $60 left. 
How much had I at first? 

12. J of James’s money is \ of Henry’s money. What 
part of Henry’s money is all of James’s money? If 
James has $150, how much has Henry? 


LESSON 76 

1. If 12 curtains cost $17.76, what will 28 curtains cost 
at the same rate? 

2. If 12 umbrellas cost $16$, what will 17 umbrellas 
cost at the same rate? 

3. What must I pay for 36 yards of muslin, if 6 yards 
cost $$$? 

4. How long will it take a man to plow 13 acres of land, 
if he plows 5 acres in 3f days? 

5. What will 48 arithmetics cost at the rate of 4 for 

$ 21 ? 

6. If 3 tons of hay cost $40, what will 19 tons cost? 

7. If 4 shawls cost $3|f, what will 21 shawls cost? 

8. If 4 tons of hay cost $52, what will 9j* tons cost? 

9. If 6 yards of carpet cost $2|f, what will 10^ yards 
cost? 

10. A gave $62 for flour at the rate of 2 barrels for 
$15^. How many barrels did he buy? 

11. If 3J bushels of chestnuts cost $5, how many 
bushels can be bought for $90? 

12. If 4 bushels of nuts cost $13, what will 8f bushels 
cost? 


54 


ONE HUNDRED LESSONS 


LESSON 77 

1. If f of a yard of cloth cost 80 cents, what will a yard 
cost? What will 4 yards cost? 

2. If f of a barrel of sugar cost $8, what will 10 barrels 
cost? 

3. If I pay $12 for 1| barrels of flour, what will 8 barrels 
cost? 

4. A horse cost 6 times as much as a cow. If f of the 
cost of the cow is $18, what did the horse cost? 

5. If f of a yard of cloth cost $Jjj, what will 8 yards 
cost? 

6. If | of a hundredweight of sugar cost $6, what will 
8 hundredweight cost? 

7. If f of a ton of hay cost $10, what will 7 tons cost? 

8. $96 is f of what I paid for a horse. What will 8 
horses cost at the same rate? 

9. A schoolboy writes 40 pages in his tablet in 6§ days. 
At the same rate what does he write in a term of 180 days? 

10. If 3J acres of land cost $299, what will a farm of 
48 acres cost? 

11. If H bushels of grain cost $4.62, what will 18 
bushels cost? 

12. If 7{ tons of coal cost $23.20, what will 24 tons cost? 

LESSON 78 

1. If 8 pounds of coffee cost $1.44, what will 13f pounds 
cost? 

2. If a man earns $26 in 8 days, what will he earn in ^ 
of a day? 

3. If a man walks 8§ miles in 2 hours, how far will he 
walk in 8^ hours? 


IN FRACTIONS 


55 


4. If a vessel sails 20 miles, in 3 hours, how far will it 
sail in 484 hours? 

5. If 3 yards of cloth cost $4.44, what will 7J yards 
cost? 

6. If 7 barrels of cider cost $100, what will 9 barrels 
cost? 

7. If 8 tons of coal cost $33|, what will 134 tons cost? 

8. If 6 acres of land cost $1182, what will 13f acres 
cost? 

9. If 8 tons of hay cost $106, what will 3£ tons cost? 

10. If 23 pounds of sugar cost $1, what will 804 pounds 
cost? 

11. If 14 bushels of oats cost $8.40, what will 13J 
bushels cost? 

. 12. A farm costs $96 an acre. If 1*4§ acres were sold 
at a gain of $10 an acre, for what sum were they sold? 

LESSON 79 

1. If 8| acres of land cost $206|, what will 9J acres cost? 

2. If 13f cords of wood cost $414, what will 184 cords 
cost? 

3. If 16| pounds of sugar cost $1.32, what will 194 
pounds cost? 

4. If 354 yards of cloth cost $26f, what will 15f yards 
cost? 

5. If 84 barrels of rice cost $764, what will 18f barrels 
cost? 

6. If 6f bushels of potatoes cost $5f, what will 194 
bushels cost? 

7. If 9 sheep cost $164, what must 1 P a y for a cow that 
costs 16f times as much as a sheep? 


56 


ONE HUNDRED LESSONS 


8. If 81 tons of hay cost $118$, what will 14i tons 
cost? 

9. If 7 i bushels of grain cost $10|i, what will 18J 
bushels cost? 

10. If 3J dozen oranges cost $l 3 3 o, what are lOf dozen 
worth? 

11. If 17f pounds of rice are worth $2.11^, what are 
15i pounds worth? 

12. If a farmer gives 8J pounds of butter for 16i yards 
of calico, how many yards should he get for 25f pounds 
of butter? 


LESSON 80 

1. If 4| tons of coal cost $19ii, how many tons can be 
bought for $21J? 

2. If 4f acres of land cost $1083%, how many acres can 
be bought for $123f? 

3. If 5| tons of coal cost $64i, how many tons can be 
bought for $57? 

4. If 3i barrels of flour cost $23$, how many barrels will 
$108* buy? 

5. If 4| tons of straw cost $57i, how many tons can be 
bought for $100? 

6. If 3J tons of iron cost $28$, how many tons can be 
bought for $38? 

7. If 9i bushels of wheat cost $5f, how many bushels 
can be bought for $10^? 

8. If 14i yards of cloth cost $11 §, how many yards can 
be bought for $16|? 

9. If 3J bushels of corn cost $2 T 7 6 -, how many bushels can 
be bought for $16i? 


IN FRACTIONS 


57 


10. If 3f cords of wood cost $13J, how many cords can 
be bought for $35? 

11. If 17i acres of land cost $395 f, how many acres 
can be bought for $1000? 

12 . If 74 barrels of sugar cost $77, how many barrels 
can be bought for $100? 

LESSON 81 

1. A man spent J of his money for food and J for clothes, 
and had $60 left. What had he at first? 

1 + J = 1 \. At first he had \\; so there remained 
if — rV, or T 6 g. r 6 ^ = $60. r V = $12. \\ = $144. 

2. A spent \ of his money for a farm and § of it in 
building a house, and had $1620 left. How much had 
he at first? 

3. A father gave J of his fortune to his son and -j- to his 
daughter, and had $700 left. How much was his fortune? 
What did each receive? 

4. I spent J of my money for books and J for clothing, 
and had $14 left. What had I at first? 

5. A farmer sold J of his potatoes to one man and | to 
another, and had 38 bushels left. How many bushels had 
he at first? How many did he sell? 

6. A merchant sold 1 of his stock of flour on Monday 
and \ on Tuesday, and had 34 sacks left. How many 
had he at first? 

7. I spent i of my money and lost J of the remainder, 
and then had $18. How much had I at first? 

8. § of the trees in an orchard bear apples, f cherries, 
and the rest peaches. If there are 20 more cherry trees 
than peach trees, how many trees in all? 


58 


ONE HUNDRED LESSONS 


9. | of an army were killed, J taken prisoners, and 
4800 men escaped. How many men in the army? 

10. A man sold J of his stock in a company to one man 
and f to another, and had 48 shares left. How many 
shares had he at first? 

11 . Smith sold J of his farm to Jones, ^ to Davis, and 
i to Lloyd, and had 46 acres left. What did he sell to 
each? 

LESSON 82 

1. What number increased' by its J equals 480? 

2 . What number increased by its § equals 775? 

3. What number increased by its | equals 1024? 

4. Three times a number increased by f of the number 
equals 525. What is the number? 

5. Twice my money increased by f of my money equals 
$380. How much money have I? 

6 . B is 45 years old and f of his age equals £ of his 
daughter’s age. How old is his daughter? 

7. A man bought a horse and a cow. The cow cost 
$40, which is f of what both cost. What did the horse 
cost? 

8 . After losing § of my money, I found \ as much as I 
lost, and then had $5.60. How much had I at first? 

9. A has 2 farms. One contains 48 acres, which is f 
of what the other contains. How many acres in both? 

10 . The difference between £ and f of a number is 318. 
What is the number? 

11. A’s money increased by its \ and J equals $357. 
How much money has he? 

12 . After selling § of his farm, 18 acres is f of what B 
had left. How many acres in the farm? 


IN FRACTIONS 


59 


LESSON 83 

1 . § of C’s money increased by $60 equals $540. How 
much money has he? 

2. \ the height of a tree increased by 80 feet equals 190 
feet. How high is the tree? 

3. | of a farm increased by 42 acres equals 315 acres. 
How many acres in the farm? 

4. The cost of a horse diminished by J of the cost and 
$320 is $2710. What did the horse cost? 

5. A sum of money diminished by f of itself and $120 
equals $4880. What is the sum? 

6 . A number increased by 6 times itself and 120 equals 
974. What is the number? 

7. Having a farm, I sold f of it and afterward bought 
80 acres, and then had 340 acres. How many acres had 
I at first? 

8 . The cost of a house increased by its J and $60 equals 
$4860. What is the cost of the house? 

9 . The cost of a farm diminished by its J and $180 
equals $4620. What is the cost of the farm? 

10. A house and lot cost $9800 and § of the cost of the 
lot plus $180 equals $1300. What is the cost of each? 

LESSON 84 

1 . A’s money increased by $258 equals 4 times his 
money. What,is his money? 

2. Four times the length of a field, diminished by 40 
rods equals twice the length. What is the length in feet? 

3 . § of a farm, diminished by 48 acres, equals f of the 
farm. How many acres in the farm? 

4 . Five times a number, plus 810, equals twice the 
number. What is the number? 


60 


ONE HUNDRED LESSONS 


5. Jones sold 56 acres more than J of his farm and had 
| of it left. How large was his farm? 

6. The cost of 8 barrels of flour equals the cost of 4J 
barrels, increased by $24.75. What is the cost of one 
barrel? 

7. The cost of f of a ton of hay is $3} more than the 
cost of | of a ton. What will 18 tons cost? 

8. The cost of 8 tons of coal is $11 ^ more than the cost 
of 4f tons. What will 5 tons cost? 

9. Three times James’ money increased by its f and 
$968 equals 5 times his money. How much has he? 

10. j of a number, increased by 48, equals J of the 
number, increased by 84. What is the number? 

LESSON 85 

1. Two fields contain 96 acres. If one is 3 times as 
large as the other, how many acres in each? 

2. Two men have $1092. One has 6 times as much as 
the other. How much has each? 

3. A farmer had 456 bushels of wheat and oats. He 
had 5 times as much oats as wheat. How many bushels 
had he of each? 

4. The sum of two numbers is 875 and one number 
equals $ of the other. What are the numbers? 

5. A house and lot cost $7500. The cost of the lot was 
i of the cost of the house. What did each cost? 

6. A farmer raised 1295 bushels of corn and sold part 
of it. What he sold was j of what he kept. How many 
bushels did he sell and how many did he keep? 

7. The sum of two numbers is 896. One number is 1J 
times the other. What are the numbers? 


IN FRACTIONS 


61 


8. A and B together earned $870. A earned 1J times 
as much as B. What did each earn? 

9. In two piles of wood there are 216 cords. One pile 
is | as large as the other. How many cords in each? 

10. A man’s salary is $975 a year. He saves § as much 
as he spends. How much does he save in 4 months? 

LESSON 86 

1. Two fields contain 98 acres. One field is 10 acres 
larger than the other. How many acres in each? 

2. A has $75 more than B, and both together have 
$1725. How much has each? 

3. The sum of two numbers is 1056 and their difference 
is 70. What are the numbers? 

4. The sum of two numbers is 1393 and their difference 
567. What are the numbers? 

5. The sum of two numbers is 92|J and their difference 
64^V- What are the numbers? 

6. A farmer had equal amounts of wheat and rye. He 
sold 86 bushels of rye and 72 of wheat and had 482 bushels 
in all left. How many bushels of each had he left? 

7. A house and lot cost $4500. The house cost 4 times 
as much as the lot, plus $500. What did each cost? 

8. In two piles of wood, there are 392 cords. If J of 
the larger pile equals the smaller pile, how many cords in 
each? 

9. A man earns $1200 a year. If § of what he spends 
equals what he saves, what does he save each year? What 
does he spend? 

10. A horse and carriage cost $245. The carriage cost 
$5 less than J as much as the horse. What did each cost? 


62 


ONE HUNDRED LESSONS 


LESSON 87 

1. A horse and cow together cost $210, and J the cost 
of the cow equals } of the cost of the horse. What did 
each cost? 

2. Walter and Miles together have $225. If f* of 
Walter’s money equals § of Miles’ money, how much has 
each? 

3. An organ and piano cost $975. If | of the cost of 
the organ equals J of the cost of the piano, what did each 
cost? 

4. \ the number of pine trees in a forest equals J of 
the number of hemlocks. If there are 1296 trees in all, 
how many are there of each kind? 

5. A father left to his two children $3525. If § of one’s 
share equals f of the other’s share, how much did he leave 
to each? 

6. John and Henry together dug 360 bushels of pota¬ 
toes. If J of what John dug equaled \ of what Henry 
dug, how many bushels did each dig? 

7. Two sacks of flour have the same ratio as 3 and 2. 
If there are 200 pounds of flour in both, how many pounds 
in each? 

8. Two farms have the same ratio as 3 and 5. If there 
are 464 acres in both, how large is each? 

9. Two men bought 480 bushels of corn for $360. If 
one paid $144, how many bushels should he get? 

10. The sum of two numbers is 861, and their ratio is 
the same as that of J and What are the numbers? 


IN FRACTIONS 


63 


LESSON 88 

1. A man lost f of his money and then found 3 times 
as much as he lost and then had $936. How much had 
he at first? 

2. A lot cost $800 and § of its cost is f the cost of the 
house. What is the cost of both? 

3. After losing | of his money, $180 was § of what 
James had remaining. How much had he at first? 

4. The difference between f and J of my money is 
$37.50. How much have I? 

5. A piano cost $800 and f of its cost is If times the 
cost of a pianola. What is the cost of the pianola? 

6. 456 bushels is f of fa of a farmer’s crop of oats. How 
many bushels has he? 

7. I gained § of its cost by selling my automobile for 
$1575. What did it cost? 

8. After spending -f of his money for board and for 
clothes, Walter had $124 left. How much had he at 
first? 

9. How much will 8 men earn in 4f days at $2f per day? 

10. Two men together earn $1235. If one earns f as 
much as the other, what does each earn? 

11. A man spent $60 more than f of his money and 
had $339 left. How much had he at first? 

12. If 3f yards of ribbon cost 26J cents, what will 7f 
yards cost? 

LESSON 89 

1. If you do a piece of work in 8 days, what part of it 
do you do in one day? In 2 days? 

2. A can do a piece of work in 4 days and B in 6 days. 


64 


ONE HUNDRED LESSONS 


What part can each do in a day? What part can they 
together do in one day? 

3. If you cut J of a cord of wood in a day, in what time 
can you cut a cord? If you cut f of a cord a day? 

4. If A and B together mow T 6 T of a field of grass in a 
day, in what time can they mow all of it? 

5. James can build a fence in 6 days, and Thomas in 
8 days. In what time can both together build it? 

6. One carpenter can build a house in 25 days and an¬ 
other in 20 days. In what time can they build it, working 
together? 

7. A cistern has two pipes by one of which it can be 
filled in 12 hours and by the other in 16 hours. In what 
time can both fill it? 

8. A can dig a ditch in 4 days. B in 6 days, and C in 
8 days. In what time can they all dig it, working to¬ 
gether? 

9. George and Samuel together paint a barn in 16 days. 
George can paint it in 24 days. In what time can Samuel 
alone paint it? 

10. Two men make a tool chest in 10 hours. If it 
would take one man 25 hours to make it, in what time 
can the other do it? 

11. A ton of hay lasts a horse and cow 8 weeks. If 
the horse can eat it in 20 weeks, in what time will the 
cow eat it? 

12. A, B, and C do a piece of work in 8 days, A and B 
in 12 days, and B and C in 18 days. In what time can 
each do it alone? 


IN FRACTIONS 


65 


LESSON 90 

1. John gave Harry 64 cents which is J of what he had 
left and } of what Harry then had. How much had each 
at first? 

2. If a 12-foot pole casts a shadow 3} ft. long, how long 
a pole will -ast a shadow 22} ft. long? 

3. A man lost } of his money and then found } of what 
he lost, and had $108. How much had he at first? 

4. § of the cost of a house is $600 more than } of its 
cost. What did the house cost? 

5. Anna had 24 apples and Alice had £ as many. How 
many times Alice’s number equals Anna’s? 

6. If § of a yard of carpet cost $1}, how many yards 
can be bought for $57}? 

7. If 16 men do a piece of work in 27} days, in what 
time can 24 men do it? 

8. I bought a half interest in a grocery and at the end 
of a year sold } of my share for $480. What was the entire 
grocery worth at that rate? 

9. A man spent }, *, and } of his money, and had $375 
left. How much had he at first? 

10. The difference between two fractions is }}, and 
one of them is f. What is the other? 

11. I gain } by selling my horse for $183}. What did 
the horse cost? 

LESSON 91 

Reduce to improper fractions: 

3* 17* 34} 19} 1371 

5* 25* 18} 26} '284* 


66 


ONE HUNDRED LESSONS 


Reduce to whole or mixed numbers: 


1 i- 

H 1 

6 4 5 

TF~ 

-w 

4 6 0 

re 

1|8 

w- 

3 6 5 

Tir 

3 0 2 

894 

Reduce to lowest terms: 




8 0 
iyy 

6 0 

THIS 

18 0 

ST6 

ill 

9 5 

yo 

5 6 

yyy 

iVs 

tA 

AV 

1 44 

Red ce: 

i> §> 4> 

A to 72ds. 




i; A> ri to 96ths. 

}, }, l f to 112ths. 
b b yV A to ISOths. 
b b f> yi to 84ths. 
i> i) yi> iJ to 120ths. 
b b 1; A to 90ths. 
h b h A to 80ths. 


Add: 


LESSON 92 


i + it + A + A + ll 
I + f + A + A + tt 

£o + y 6 o + * + t + 4 

A + A + A + 4 + 4 


26^ + 32tf + 48A 
47 § + 91* + 18* 
96 f + 72 A + 46H 
384 + 18 A + 74| 


Subtract: 


* - i I - ! 25 - 8A 63* - 18* 
it - A H - i 34 - 17A 91H - 36 r 6 o 

Multiply: 

to X f| X A X A 498 X 36§ 

it X yif X if X A 2 o 664 X 28f 

g-y X A X ii X ft 610 X 84| 

if X if X ti X f| 703 X 47f 


IN FRACTIONS 


67 


Divide: 




4*-M 
10 if 


18f + 9f 

m + 6j 


LESSON 93 


Add: 

b i) i\> zb) H> tJ- 

§> 4J b 8> 1Z) zb I h lb 

b h l) b tj * tV? * 2¥j 2T; sV 

i> §> l) i) i> to) TZ) *> iz) zb li* 

418J, 3671§, 30*, 4981J, 135* 

7583J, 418J, 756|, 48§, 715*, 486* 
7984i, 3867f, 715* 384f, 38* 


Subtract: 

13 _ 5 1—2. 

2 4 T S' 8 1 

1 1 _ 1 2 9 _ 3 

T8 4 30 4 

Multiply: 

324f X 186 
481 f X 175 
682 X 34f 

356f X 128* 


401| - 182i 403^ - 215* 

385f - 216* 621* - 327* 

n X is x 6f X 34 
3i X 5* X 8f X 2f 
1* X 74 X 6f X 8J 
4f X 9* X 31 X 7i 


IMUM/iP * 

U + i if + 7} 9,856 + li 172i 4- 18| 

H + liltH+H 84| + 4ftA Ar + 36 


LESSON 94 

1. Find perimeter of a room 48 ,V ft. long and 29| ft. 
wide. 

2. Find perimeter of a square field 258§ ft. on each side. 

3. Find perimeter of a lot 186f ft. long and 1454 ft. 
wide. 


68 


ONE HUNDRED LESSONS 


4. Find perimeter of a triangular field 81 ££ ft. on a side^ 

5. Find perimeter of an octagonal field 26f ft. on a side. 

6. Twenty men build a house in 16 days. In -what 
time can 15 men build it? 

7. A, B, and C have $216. A and B have $128. A 
and C have $134. How much has each? 

8. I spent £ of my money and had $49 left. How 
much had I at first? 

9. A man spends f of each day in work. In what time 
will he work 15 full days? 

10. Four tons of coal cost $8|. How many tons can 
be bought for $171? 

11. The perimeter of a square is 44£ inches. If each 
side were 54 inches shorter, what would be its perimeter? 

12. If shoes that cost $3f are sold at £ of cost, how many 
pairs can be bought for $117? 

LESSON 95 

1. John’s money is § of James’ money and James’ 
money is £ of George’s money. What part of George’s 
money is John’s? 

2. At 10J miles an hour, how far can a man ride on a 
bicycle by riding 4-J hours in the morning and If hours 
in the afternoon for 3 successive days? 

3. A horse was sold for $210. This was f of its cost. 
What did the horse cost? 

4. A family uses £ of a sack of flour in 2 weeks. How 
long will 18 sacks last? 

5. A furniture dealer lost T V of its cost by selling a 
couch for $14.85. If he had gained f°r what would 
he have sold it? 


IN FRACTIONS 


69 


6. I have $24J. This is T \ of what my brother has. 
How much has he? 

7. $140 is 4 of the cost of a horse, and a carriage cost 
i as much. What is the cost of both? 

8. I spent ■§■ of my money and had $65 left. How 
much had I at first? 

9. There are 30i sq. yd. in a square rod. How many 
square yards in 36 sq. rd.? 

10. At the rate of $f a yard, how many yards of carpet 
can be bought for $18.75? 

11. A bought land for $8000 and sold it at a gain of T V 
If he gained $2 on each acre, how many acres were in the 
tract? 

12. A farmer received $4£ for 6 lb. of butter. What 
did he get per pound? 

LESSON 96 

1. A field containing 8§ acres was divided into plots 
of 1| acres each. How many such plots were there? 

2. A man sold a horse for $210 and a buggy for f as 
much. What did he get for both? 

3. A does a piece of work in 25 days. How much of the 
work does he do in 15 days? 

4. I spent § of my money for books and \ of it for paper 
and had 25 cents left. How much had I at first? 

5. I had $10 and spent $2f for car fare and $lf for 
food. How much had I left? 

6. Harry has $4.15 and his brother has | as much. 
How much have both? 

7. A and B together own f of a factory valued at 
$24,000. If their shares are equal, what is the value of 
each? 


70 


ONE HUNDRED LESSONS 


8. What is the perimeter of a field 18J rd. long and 
14| rd. wide? 

9. John’s money is f of Charles’ money and Charles’ 
money is ^ of James’ money. What part of James’ 
money is John’s? 

10. How many hats at $2| each can be bought for $39? 

11. A knife is worth $I 9 0 and a slate £ a. much. What 
are both worth? 

12. At the rate of \2\ miles per hour how far will a man 
ride in 12J hours? 

LESSON 97 

1. A merchant owning | of a store sold J of his share. 
What part of the store does he still own? 

2. A man paid $9.60 for a railroad ticket at the rate 
of 2\ cents a mile. How far was he going? 

3. A cistern will hold 270i gallons. How long will it 
take to fill it with water running through a pipe at the 
rate of 2f gallons a minute? 

4. Gold is 19i times as heavy as water. A cubic foot 
of water weighs 62J lb. What will a cubic foot of gold 
weigh? 

5. If a man can row 6 mi. an hour in still water, how 
far can he row in 8 hours down a river which flows 2\ miles 
an hour? 

6. Add J, T V, and -,V 

7. How many feet in 16J rods (16J ft. = 1 rd.)? 

8. A merchant gained £ by selling 16 barrels of flour 
at $7.20 a barrel. What did the flour cost? 

9. A bedroom suite cost $42f. What would 16 suites 
cost at the same rate? 

10. What will 8f lb. of meat cost at 16 cents a pound? 


IN FRACTIONS 


71 


11. Jones had 8§ acres in corn. If it yields 48 bushels 
to the acre, what will be the amount of his crop? 

12. How many hours in 53f days? 

LESSON 98 

1. Two men are 217 miles apart. They travel toward 
each other, one traveling 3} miles an hour, the other 4} 
miles. How soon will they meet? 

2. A boy who lives If miles from school will walk how 
many miles in a week in going to and from school? 

3. Three men bought an automobile. One paid $134^; 
another $13f more than the first, and the third as much 
as both. What did the automobile cost? 

4. A farm contained 400 acres. After 2 plots contain¬ 
ing 97f acres and 116f acres, respectively, were sold, how 
many acres remained? 

5. After selling f of his crop, a farmer had 798 bushels 
of corn left. How many bushels had he at first? 

6. I bought 15 yards of calico at 6J cents a yard and 12 
yards of gingham at 8J cents a yard. I gave the clerk $5. 
How much change should I receive? 

7. Find the perimeter of a hexagonal room 16£ feet on 
69 iCli side. 

8. A man pays a yearly rent of $160. What will be his 
rent for 7} months? 

9. A man lost f of his money and afterwards found \ 
of it and then had $68. How much had he at first? 

10. I bought 84 acres of land at $26^ an acre and sold 
it for $34f an acre. What did I gain? 

11. When oranges are 12} cents per dozen, how many 
dozen can be bought for $4.93f? 

12. The product of two numbers, diminished by 86|, 
is 225}, and one number is 18. What is the other number? 


72 


ONE HUNDRED LESSONS 


LESSON 99 

1. A man earned $67 J by working for $2f a day. How 
many days did he work? 

2. If a man travels 340 miles in 8f days, how far will 
he travel in 11 days? 

3. Find the value of f X 5f -f- (2f — 1J). 

4. Divide fa of 1 fa by § of 4§. 

5. Find the value of 1J X If i X 11. 

6 . A, B, and C have $85Jft. A and B have $45^V A 
and C have $58j. How much has each? 

7. Jones had 18J acres sowed in wheat which yielded 
48 bushels per acre. He sold § of it at 56 cents a bushel. 
What did he receive for it? 

8 . George has $112J. James has § as much, plus $25. 
How much has James? 

9. Eight men do a piece of work in 17J days. In what 
time can 5 men do it? 

10. A farm was bought for $7000 and sold at a gain of 
If the gain is $4 on each acre, how many acres in the 

farm? What did it cost per acre? 

11 . I spent | of my money for clothing and J of it for 
food and had left $10f. How much had I at first? 

12 . A lot contains 121J sq. rd. and another f as much. 
How many square yards in both (30J sq. yd. = 1 sq. rd.)? 

13. If $4^ is fa of my money, how much have I? 

LESSON 100 

1 . $36 is $20 less than } of my money. How much 
money have I? 

2 . $54 is $12 more than f of my money. How much 
money have I? 


i 


IN FRACTIONS 


73 


* 

3. I shingled 4 of a roof yesterday and J to-day. What 
part have I to do to-morrow? Which day’s work is the 
greatest? 

4. A large pipe can fill a cistern in 10 hours, and a small 
one in 24 hours. In what time can both together fill it? 

5. Which is the greatest and which the least; f, 4$, 
or f? 

8 . From a farm containing 413§ acres there was sold 
37^ acres, 64 T 5 g- acres, and 594 acres. If the remainder is 
worth $10,112, what was the value of the entire farm? 

7. A silver dollar weighs 4124 grains, but only T 9 7 of it 
is pure silver, the rest being copper. How many grains 
of each metal in it? 

8 . A, B, and C can do a piece of work in 12 days; A and 
B in 18 days; A and C in 27 days. How long will it take 
each to do it? 

9. A person spent and J of his money, and had 
$225 left. How much had he at first? 

10. Two men can build a house in 20 days and one 
alone can build it in 30 days. In what time can the other 
build it? 

11 . The difference between § and f of a number is 36. 
What is the number? 

12 . A man owning f of a factory sells | of his share for 
$3600. What is the value of the factory? 

13. A bought 63^ bushels of oats at 56 cents a bushel 
and sold 4 of it at 70 cents a bushel and the rest at 654 
cents a bushel. What was his gain? 

14. My father was 42f years old at my birth and I was 
2 4 years old when my brother was born. I am now 24J 
years old. How old are my father and brother? 






\ 


ANSWEKS 


lesson 36.—H* H* i|* **>, “ 8 , *fi, &«i ; 

H 1 . -W-, H 1 , H 3 -, H s -, H 1 , A IS 4 a » -P, 8 i¥, 4 ! 4 , 2 ! 4 , 

2.6 9 5 1 0 4 5 5. 

*7 T 7 ' 8 * 

Lesson 37.—19i, 22J, 17f, 21£, 24f, 16*, 13, 15f, 32f, 
32, 241, 29, 10ft, 8 t V, 23, 18*, 29f, 39$, 16J, 38f, 19f, 
18i, 23, 29f, 14|, 19|, 241, 26. 


Lesson 38.—|, 1, f, 1, J, J, §, *, *, *, §, i, l , 1> f> 


175231 4 3 7 8 6 35 

67 ¥7 If7 «?7 T, T7 1T7 TIT, 1^7 *2, 87 

Tnccfin 40_2 3 5 1 3.7 .3 7 28 2_9 2 6. 3 1 2_5 

wesson fiu, 4 , g , fo, i» 37 6 ? 37 t ) 47 


. 7 4 

'7 2 7 


. 14 6 21 

7 2*7 ?*, -24 7 *l 


10-9 3 16 

8 TJT T 87 TS7 1 8 
3 1 4 9 . 2 5 3.2 _ 6 _ _ 

T87 T^7 187 * (T 7 4 0 7 4 0 7 4 0 


4*7 V, M*, AA -H 1 , AA A-; % 61, 8*, 91, 8f, 71, 
9f, 15, 6, 9*, 24, 36J, 16*, 134, 421, 25, 3f, 74|, 24|, 
32f, 37j; I, A, *, *7 i, I, A f A §7 Si if, iA b ib b 
I? -337 i7 A 7 I 7 1 5 ff, ft, A, ft? A? A 7 St, A 7 A; 

A? §8 7 Si Tib A 7 A; A? U 7 St; ff, II? ft; SA A 7 

21 H, ii; «, «, it; if, 

. 16 20 21 22. 24 25 14 

7 2*7 8*7 2*7 ¥*7 3 0 7 T(T7 3 0 7 

11; ii fi7 A, H; 1*7. »7 St, H. 

Lesson 41. —1A, 1 A, A 5 *, 1A, A, A 5 *, Ai, if, AV 
A 3 0, AV, A, A 5 8 7 a, 1A, lit, A, AS, AS, AV, Ai 
Lesson 42.— A 9 o, Iff, AV, 2JJ, 2f, 2*V, AV, If if, 
2A, 1 AV, 2|f, 2f|-,'3A, 3, A, 2ff, AS, 2*, 2*, 2A, 
9A, 13*7 12Ji 17ff. 


Lesson 43.-2014, 229*, 2,572|f, 1,424*1, 947*, 
1,67841, 2,386*, 2,40*1, 2,014*, 1,979ft, 1,9784, 
1231H, 206AV, 257AV, 34*, 33fff, 38*, 28*VV* 
Lesson 44.—*, *, *, A, A, A, A, A, A, A, */ A, 
A, A, A7 ii *, A, A, A, SA 

75 


76 


ANSWERS 


lesson 45.-H, H, U, *, ih A, H> l h H, A, A. 
t 3 i» A, t}i }, Hi Hi ill h A, A, ill 11- 

Lesson 46.— 217*, 316i, 234 A, 205J, 558}, 173f, 313f, 
36If, 268-1, 281J, 242}, 142*, 113}, 245A, 244}, 206A, 
343}}, 290}, 999*, 999*»*, A, 998**, 9,090}, 6,059*. 

Lesson 47.-217}}, 316*, 234*, 205}, 558||, 173|, 
313}}, 361}}, 268}}, 281}}, 242§, 142}}, 172*, 254*, 
251}}, 274}}, 348}}, 298f}, 249-}, 990}. 

Lesson 48.— 1 *\, f|, 1 *, **, *, 1*V, 6}}, 2|, 12*, 
2}, 83}}, 23}}, 707}, 510}, 698*, 197*. 

Lesson 49.—$3}, 39} yd., 38f lb., $9*, 26*, $130, 
264} ft., 96* ft., 43} ft., 271}} ft., 156f acres, }, $59}, 
41} acres, * rd. 

Lesson 50.-16, 40, 48, 60, 40, 72, 20, 45, 18, 45, 66, 54, 
124, 44, 55, 70, 8, 44, 38, 12, 15, 24, 14, 42, 60, 63, 15, 51, 
36, 18, 105, 175. 

Lesson 51.—16}, 26§, 20§, 9}, 17}, 37}, 14}, 8}, 6|, 9}, 
16}, 7}, 14}, 17|, 24f, io} ; 8}, Ilf, 16f, 4}, 5|, 9}, 11}, 
9f, 6*, 9}, 20*, 14}, 16}, 22}}, 6§, 26}. 

Lesson 52.-}, f, *, }, f }, }}, }, *, }, *, }, *, i 
*, 5, 6, 2, If}, 2}, 18, 17f, 34J, 67}, 22}. 

Lesson 53.—132}, 30}, 100}, 520}, 144}, 175}, 205}, 
61*i H7}, 273}, 217}, 81*, 247}, 531}, 225, 231, 157}, 
582§, 342j}, 555}, 666f, 857}, 407*. 

Lesson 54.-13,221, 19,684, 12,369, 19,719, 15,036 
36,449, 13,430, 25,459, 16,041, 16,544, 19,956, 28,072' 
24,163}, 28,352}, 17,176f, 29,506}, 31,676}, 21,530}, 
50,811}, 62,443}, 31,831}. 

Lesson 55.-56,525, 33,579, 12,013}, 72,693, 24,864, 


A NS WEES 


77 


22,150, 32,552, 5,092, 24,152$, 22,625, 21,484§, 7,168|, 
64,592$, 27,731,18,180|, 40,150,39,312$, 30,795 J, 22,663}, 
34,625, 33,226$. 

Lesson 56.-2$, 4f, ||, }|, $, 16, $$, $, 2$, $, }}, $, 

1152 1 11 6 1513 

T> TF) T8- 

Lesson 57.-$684, $1.40, $2,725J, $1014, $28.12*, $2.30f, 
$2.15J, $2,298f, $514i, $69.86§, 448 hr., 341 da., 454 oz., 
1,105 min., 441, 5G6 cents, 3,504 da., 861 mo.. | he plays 
and works T \, $5, $l*f. 

Lesson 58. —If, l^V? linr> l*f> If; If; 4; 7 %, 

If, 2|, If, 1}, 3f, 6f, Ilf, If, 3f, t 9 0 , 6, 2f, m, 4- 

Lesson 59.-1$, 1$, 2 $, ||, 2*, 1*, i\, l, A, lil, Ih 

H, If, ih i, t. A, 11- 

Lesson 60.-738, 276, 132, 590, 834, 252, 432, 540, 228, 
475, 522, 158, 375, 272, 465, 375, 384, 112, $, $,$,$, i, *. 

Lesson 61.— *, T | T , 1$$, $’> i, tIt. iV. t$s> $> t$> 
18||, 23f, 8,370*, 7,096$|, 5,915$$, 17,150*, 8,587*, 
123,902*, 10,852|, 6,070|3- 

Lesson 62.-21, 54, 228, 288, 380, 7,345$, 10,105$, 
24,592$, 78,018$, 90,572, 8, 39, 25, 1,005$, 10,411$, 
45',936, 62,237$, 30,211$, 56,136, 11,200. 

Lesson 63.— |, $, 1*, l$f, 1|$, If. A 10, *, 2$®, 9$, 
2 |i 1$, f, If, 2$. 2$|, $, 2, III, 15#, l$n, m, AiV 

Lesson 64. —40 da., 45 min., 7, 5 da., 9 yd., 5, $52$, 
8 tons, 4 acres, 26 bar., 3f da., 1$, 29 prs., 40 oranges. 

Lesson 65.—$2$, 13$ yd., 20 cents, 3, 30 mi., $1.65, 
36 doz., 21, 95 cents, 198, 38 mi., 5 tons, 10$ lb. 

Lesson 66.—-4~; i-y- 5 , J-y* 1! ,", *¥-*. J “ 3 > 

j}i, 93§, 197$, 3061, 433$, 340$, 963, 714$, 632|, $$, 


78 


ANSWERS 


impossible, }, f, *, *, }, *, 2f, 1*, Iff, 11, 34*, 30*, 
38f|, 64|3, *, J|, *, *, 8|, 4J, 4ff, 4||, *, *, J, 
4,268J, 7,338, 3,078§, 3,9254, 1*|, 2|, H|, If, 4f, 18, 
2M, 4- 

Lesson 67.-139}, 195ft, 151|, 184}f, 1,1134}, 1,433*, 
1,188*, 1590JJ, 576J1, 390f}, 84ff, 245 3 '*, 4711, 168f, 
1844, 197*, 660, 1,002, 3,874, 3,632, 4, 54, 24, 3, 1*, 14, 
44, 4*, 156f, 73f, 90*, 784. 

Lesson 70. f, f, §, f, 4, }, f, f, *, }, f, f, f, §, }, f, 
$134,20 cents, 16}, $20, $172, $3Sf, $9, 374 cents, 48 cents. 

Lesson 71—$148, $11.50, $764, $104, $12.96, $143, 
$129.50, $360, $15.84, $17.76, $20.25, $108, $150, $14.40, 
$130.50, $40.50. 

Lesson 72—16, 12, 30, 14, 36, 10, 18, 16, 36, 21, 20, 15, 
21, 32, 25„ 25, 40, 32, 56, 28, 56, 40, 81, 72. 

Lesson 73.—$240, $3, $128, $3,600, 65 bu., 132 mi., 304 
sq.yd.,$720, $96,20 sacks, $5.76, $18.15, $64 and $256, $28. 

Lesson 74.—200, 144, 120, 98, 216, 200, 360, 630, 500, 
320, 450, 360, 378, 496, 444, 1,170, 525, 1836, 820, 1,152. 

Lesson 75.—$40, $14.95, $5.52, $8,803, $38.40, 63 mi., 
$294, $94, 288, $74, $84, $250. 

Lesson 76—$41.44, $23}, $4*, 9} da., $28}, $2534, 
$20If, $119|, $5*, 8 bar., 60 bu., $28*. 

Lesson 77.—$4, $120, $80, $180, $11|, $60, $112, $864, 
1080 pages, $5,376, $19.80, $76.80. 

Lesson 78.—$2.20, $1§, 36| mi., 3234 mi., $10.73, $128}, 
$56*, $2,6844, $42§, $ 34 , $8,324, $1,523}. 

Lesson 79.—$224, $54}, $1.56, $11*, $168}, $15|, $29}, 
$195}, $284, $4*, $1.83, 514 yd. 


ANSWERS 


79 


Lesson 80. —5 tons, 5 acres, 4f tons, 16 bar., 8 tons, 4f 
tons, 17 bu., 21 yd., 21f bu., 8j cords, 43|£ acres, bar. 

Lesson 81. —$16,200, $1,500 fortune, $24, 60 bu. at first, 
56 sacks, $36, 150, 18,000 men, 126 shares, 120 acres in 
farm. 

Lesson 82.— 360, 465, 640, 140, $160,12 yr., $140, $8.40, 
176 acres, 9,540, $252, 243 acres. 

Lesson 83.— $720, 220 ft., 364 acres, $4,545, $12,500, 
v 122, 650 acres, $3,600, $7,200, $1,680 lot. 

Lesson 84. —$86, 330 ft., 108 acres, 270, 840 acres, $6.75, 
$288, $16$704, 216. 

Lesson 85. —24 acres and 72 acres, $156 and $936, 76 
bu. and 380 bu., 350 and 525, $1,250 and $6,250, 555 bu. 
and 740 bu., 384 and 512, $348 and $522, 96 cords and 120 
cords, $130. 

Lesson 86. —44 acres and 54 acres, $825 and $900, 493 
and 563, 413 and 980, 14J and 78£, 234 bu. and 248 bu., 
$800 and $3,700, 147 cords and 245 cords, $480 and $720, 
$45 and $200. 

Lesson 87 — $60 and $150, $100 and $125, $375 and 
$600, 486 and 810, $1,410 and $2,115, 144 and 216, 80 lb. 
and 120 lb., 174 acres and 290 acres, 192 bu., 369 and 
492. 

Lesson 88.— $702, $2,880, $1,200, $250, $384, 2,394 bu., 
$1,125, $160, $981, $380 and $855, $665, 51J cents. 

Lesson 89.— 2^ da. (No. 4), 3f da., 11J da., 6f hr., l^J 
da., 48 da., 16f hr., 13J week.; 14f, 24 and 36 da. 

Lesson 90.— $1.90 and $1.92, 84 ft., $144, $9,000, If 
25§ yd., 18i da., $1,600, $1,000, |, $153. 


ANSWERS 




80 


Lpsqnn Q1 83 8 * 20 9 280 1 04 1 6 7 16 9 1 3 4 8 2 7 

wesson vi. 2F , 1W , 12 , iri s > s~t 


s « 3 , 351, 21J, 24f, 261, 43, 24J, 161, 331, 28J, 44* f, 


7 151112384 6 5 9 

TT> T?> 39) f) T7; 13) 1 


Lesson 92.-lf J, 2f|, 2|J, 21, 108, 157A, 215JJ, 132ff, 
A. fl. II. 41. 161, 16*, 34»|, 551, A, A, A, A. 18,260, 
16,074, 51,728, 33,626f, 1*, 1*, *, If, 21f, 7*, l§ff, 


0 7 4 

Lesson 93— 4*,5f|, If, 7*, 9,237§f, 10,0091,13,3321, 
il, 14, fl, 14, 21911, 168ft, 1874, 29314, 60,419, 84,291 §, 
23,3394, 45,742§, 1214 , 366Jf, 7561, 11651, 1*, A, *, 
111, 7,392, f|, 9§, *. 

Lesson 94.-156* ft., 1,034§ ft., 664J ft., 245} ft., 211 
ft., 21J da., $88 and $82 and $46, $245, 40 da., 8 tons, 
40| in., 39 pairs. 


Lesson 95.— |, 188* mi., $240, 45 wk., $17,321, $35, 
$3671, $91, 1089 sq. yd., 25 yd., 400 acres, 80 cents. 


Lesson 96.-6, $270, |, $3, $5ff, $6.64, $4,500, 65* rd., 
f, 15, $4|, 150* mi. 


Lesson 97.—*, 384 mi., 102|f min., 1,2031 lb., 66 mi., 
Iff, 272J ft-, $6 per barrel, $684, $1.40, 416 bu., 1281 hr. 

Lesson 98.—25ff hr., 161 mi., $5651, 185f4 A., 1026 
bu., $3.04, 961 ft-, $100, $96, $680-1, 391 doz., 171- 

Lesson 99.-24* da., 427f mi., 3*, * 2, $401 and 
$181 and $271, $310.80, $100,28 da., 350 acres costing $20 
each, $24, 6,602* sq. yd., $9. 

Lesson 100. —$64, $49, * to do and last day’s work is 
greatest, 7* hr., J is greatest and f is least, $16,546§, 
411 gr. and 3711 gr., 36 da. and 21| da. and 108 da., 
$630, 60 da., 160, $24,000, $6.74f J, 67f yr. and 21* yr. 
















































































































































































































































































































































































































































































































































































































































































































































































































































































































